812c1a2960
The elaborator produces better proof terms. This is particularly important when we have to prove the remaining holes using tactics. For example, in one of the tests, the elaborator was producing the sub-expression (λ x : N, if ((λ x::1 : N, if (P a x x::1) ⊥ ⊤) == (λ x : N, ⊤)) ⊥ ⊤) After, this commit it produces (λ x : N, ¬ ∀ x::1 : N, ¬ P a x x::1) The expressions above are definitionally equal, but the second is easier to work with. Question: do we really need hidden definitions? Perhaps, we can use only the opaque flag. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
398 lines
16 KiB
Text
398 lines
16 KiB
Text
Set: pp::colors
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Set: pp::unicode
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Assumed: f
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Failed to solve
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⊢ (?M::1 ≈ λ x : ℕ, x) ⊕ (?M::1 ≈ nat_to_int) ⊕ (?M::1 ≈ nat_to_real)
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(line: 4: pos: 8) Coercion for
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10
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Failed to solve
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⊢ Bool ≺ ℕ
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Substitution
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⊢ Bool ≺ ?M::0
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(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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⊢ ℕ ≺ ?M::0
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Substitution
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⊢ ?M::5[inst:0 (10)] ≺ ?M::0
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(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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x : ℕ ⊢ ℕ ≈ ?M::5
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Destruct/Decompose
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⊢ ℕ → ℕ ≈ Π x : ?M::4, ?M::5
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Substitution
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⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
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Function expected at
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?M::1 10
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Assignment
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⊢ ℕ → ℕ ≺ ?M::3
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Propagate type, ?M::1 : ?M::3
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Assignment
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⊢ ?M::1 ≈ λ x : ℕ, x
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Assumption 0
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Failed to solve
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⊢ Bool ≺ ℤ
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Substitution
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⊢ Bool ≺ ?M::0
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(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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⊢ ℤ ≺ ?M::0
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Substitution
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⊢ ?M::5[inst:0 (10)] ≺ ?M::0
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(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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a : ℕ ⊢ ℤ ≈ ?M::5
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Destruct/Decompose
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⊢ ℕ → ℤ ≈ Π x : ?M::4, ?M::5
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Substitution
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⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
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Function expected at
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?M::1 10
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Assignment
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⊢ ℕ → ℤ ≺ ?M::3
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Propagate type, ?M::1 : ?M::3
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Assignment
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⊢ ?M::1 ≈ nat_to_int
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Assumption 1
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Failed to solve
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⊢ Bool ≺ ℝ
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Substitution
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⊢ Bool ≺ ?M::0
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(line: 4: pos: 6) Type of argument 3 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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⊢ ℝ ≺ ?M::0
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Substitution
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⊢ ?M::5[inst:0 (10)] ≺ ?M::0
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(line: 4: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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?M::1 10
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⊤
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Assignment
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a : ℕ ⊢ ℝ ≈ ?M::5
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Destruct/Decompose
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⊢ ℕ → ℝ ≈ Π x : ?M::4, ?M::5
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Substitution
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⊢ ?M::3 ≈ Π x : ?M::4, ?M::5
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Function expected at
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?M::1 10
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Assignment
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⊢ ℕ → ℝ ≺ ?M::3
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Propagate type, ?M::1 : ?M::3
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Assignment
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⊢ ?M::1 ≈ nat_to_real
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Assumption 2
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Assumed: g
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Error (line: 7, pos: 8) unexpected metavariable occurrence
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Assumed: h
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Failed to solve
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x : ?M::0, A : Type ⊢ ?M::0 ≺ A
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(line: 11: pos: 27) Type of argument 2 must be convertible to the expected type in the application of
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h
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with arguments:
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A
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x
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Assumed: my_eq
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Failed to solve
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A : Type, B : Type, a : ?M::0, b : ?M::1, C : Type ⊢ ?M::0[lift:0:3] ≺ C
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(line: 15: pos: 51) Type of argument 2 must be convertible to the expected type in the application of
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my_eq
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with arguments:
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C
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a
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b
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Assumed: a
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Assumed: b
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Assumed: H
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Failed to solve
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⊢ ?M::0 ⇒ ?M::3 ∧ a ≺ b
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Substitution
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⊢ ?M::0 ⇒ ?M::1 ≺ b
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(line: 20: pos: 18) Type of definition 't1' must be convertible to expected type.
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Assignment
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H1 : ?M::2 ⊢ ?M::3 ∧ a ≺ ?M::1
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Substitution
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H1 : ?M::2 ⊢ ?M::3 ∧ ?M::4 ≺ ?M::1
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Destruct/Decompose
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⊢ Π H1 : ?M::2, ?M::3 ∧ ?M::4 ≺ Π a : ?M::0, ?M::1
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(line: 20: pos: 18) Type of argument 3 must be convertible to the expected type in the application of
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Discharge::explicit
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with arguments:
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?M::0
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?M::1
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λ H1 : ?M::2, Conj H1 (Conjunct1 H)
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Assignment
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H1 : ?M::2 ⊢ a ≺ ?M::4
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Substitution
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H1 : ?M::2 ⊢ ?M::5 ≺ ?M::4
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(line: 20: pos: 37) Type of argument 4 must be convertible to the expected type in the application of
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Conj::explicit
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with arguments:
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?M::3
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?M::4
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H1
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Conjunct1 H
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Assignment
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H1 : ?M::2 ⊢ a ≈ ?M::5
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Destruct/Decompose
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H1 : ?M::2 ⊢ a ∧ b ≺ ?M::5 ∧ ?M::6
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(line: 20: pos: 45) Type of argument 3 must be convertible to the expected type in the application of
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Conjunct1::explicit
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with arguments:
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?M::5
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?M::6
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H
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Failed to solve
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⊢ b ≈ a
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Substitution
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⊢ b ≈ ?M::3
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Destruct/Decompose
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⊢ b == b ≺ ?M::3 == ?M::4
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(line: 22: pos: 22) Type of argument 6 must be convertible to the expected type in the application of
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Trans::explicit
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with arguments:
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?M::1
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?M::2
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?M::3
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?M::4
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Refl a
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Refl b
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Assignment
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⊢ a ≈ ?M::3
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Destruct/Decompose
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⊢ a == a ≺ ?M::2 == ?M::3
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(line: 22: pos: 22) Type of argument 5 must be convertible to the expected type in the application of
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Trans::explicit
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with arguments:
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?M::1
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?M::2
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?M::3
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?M::4
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Refl a
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Refl b
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Failed to solve
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⊢ (?M::1 ≈ Type) ⊕ (?M::1 ≈ Bool)
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Destruct/Decompose
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⊢ ?M::1 ≺ Type
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(line: 24: pos: 6) Type of argument 1 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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Bool
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Bool
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Failed to solve
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⊢
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(?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?M::0 ≈ (Type 2)) ⊕ (?M::0 ≈ (Type M)) ⊕ (?M::0 ≈ (Type U))
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Destruct/Decompose
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⊢ Type ≺ ?M::0
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(line: 24: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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Bool
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Bool
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Failed to solve
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⊢ (Type 1) ≺ Type
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Substitution
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⊢ (Type 1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ Type
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Assumption 1
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Assignment
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⊢ ?M::1 ≈ Type
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Assumption 0
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Failed to solve
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⊢ (Type 2) ≺ Type
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Substitution
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⊢ (Type 2) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type 1)
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Assumption 2
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Assignment
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⊢ ?M::1 ≈ Type
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Assumption 0
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Failed to solve
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⊢ (Type 3) ≺ Type
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Substitution
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⊢ (Type 3) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type 2)
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Assumption 3
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Assignment
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⊢ ?M::1 ≈ Type
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Assumption 0
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Failed to solve
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⊢ (Type M+1) ≺ Type
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Substitution
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⊢ (Type M+1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type M)
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Assumption 4
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Assignment
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⊢ ?M::1 ≈ Type
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Assumption 0
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Failed to solve
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⊢ (Type U+1) ≺ Type
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Substitution
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⊢ (Type U+1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type U)
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Assumption 5
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Assignment
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⊢ ?M::1 ≈ Type
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Assumption 0
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Failed to solve
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⊢
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(?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?M::0 ≈ (Type 2)) ⊕ (?M::0 ≈ (Type M)) ⊕ (?M::0 ≈ (Type U))
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Destruct/Decompose
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⊢ Type ≺ ?M::0
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(line: 24: pos: 6) Type of argument 2 must be convertible to the expected type in the application of
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f::explicit
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with arguments:
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?M::0
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Bool
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Bool
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Failed to solve
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⊢ (Type 1) ≺ Bool
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Substitution
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⊢ (Type 1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ Type
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Assumption 7
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 6
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Failed to solve
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⊢ (Type 2) ≺ Bool
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Substitution
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⊢ (Type 2) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type 1)
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Assumption 8
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 6
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Failed to solve
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⊢ (Type 3) ≺ Bool
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Substitution
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⊢ (Type 3) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type 2)
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Assumption 9
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 6
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Failed to solve
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⊢ (Type M+1) ≺ Bool
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Substitution
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⊢ (Type M+1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type M)
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Assumption 10
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 6
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Failed to solve
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⊢ (Type U+1) ≺ Bool
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Substitution
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⊢ (Type U+1) ≺ ?M::1
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Propagate type, ?M::0 : ?M::1
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Assignment
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⊢ ?M::0 ≈ (Type U)
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Assumption 11
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 6
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Failed to solve
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a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ (a ⇒ b) ⇒ a ≺ a
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Substitution
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a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ (a ⇒ b) ⇒ a ≺ ?M::5[lift:0:1]
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Substitution
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a : Bool, b : Bool, H : ?M::2, H_a : ?M::6 ⊢ ?M::2[lift:0:2] ≺ ?M::5[lift:0:1]
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Destruct/Decompose
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a : Bool, b : Bool, H : ?M::2 ⊢ Π H_a : ?M::6, ?M::2[lift:0:2] ≺ Π a : ?M::3, ?M::5[lift:0:1]
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(line: 27: pos: 21) Type of argument 5 must be convertible to the expected type in the application of
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DisjCases::explicit
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with arguments:
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?M::3
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?M::4
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?M::5
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EM a
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λ H_a : ?M::6, H
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λ H_na : ?M::7, NotImp1 (MT H H_na)
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Normalize assignment
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?M::0
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Assignment
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a : Bool, b : Bool ⊢ ?M::2 ≈ ?M::0
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Destruct/Decompose
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a : Bool, b : Bool ⊢ Π H : ?M::2, ?M::5 ≺ Π a : ?M::0, ?M::1[lift:0:1]
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(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
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Discharge::explicit
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with arguments:
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?M::0
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?M::1
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λ H : ?M::2, DisjCases (EM a) (λ H_a : ?M::6, H) (λ H_na : ?M::7, NotImp1 (MT H H_na))
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Assignment
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a : Bool, b : Bool ⊢ ?M::0 ≈ (a ⇒ b) ⇒ a
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Destruct/Decompose
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a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
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Destruct/Decompose
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a : Bool ⊢ Π b : Bool, ?M::0 ⇒ ?M::1 ≺ Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
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Destruct/Decompose
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⊢ Π a b : Bool, ?M::0 ⇒ ?M::1 ≺ Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
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(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.
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Assignment
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a : Bool, b : Bool, H : ?M::2 ⊢ ?M::5 ≺ a
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Substitution
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a : Bool, b : Bool, H : ?M::2 ⊢ ?M::5 ≺ ?M::1[lift:0:1]
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Destruct/Decompose
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a : Bool, b : Bool ⊢ Π H : ?M::2, ?M::5 ≺ Π a : ?M::0, ?M::1[lift:0:1]
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(line: 27: pos: 4) Type of argument 3 must be convertible to the expected type in the application of
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Discharge::explicit
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with arguments:
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?M::0
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?M::1
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λ H : ?M::2, DisjCases (EM a) (λ H_a : ?M::6, H) (λ H_na : ?M::7, NotImp1 (MT H H_na))
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Assignment
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a : Bool, b : Bool ⊢ ?M::1 ≈ a
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Destruct/Decompose
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a : Bool, b : Bool ⊢ ?M::0 ⇒ ?M::1 ≺ ((a ⇒ b) ⇒ a) ⇒ a
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Destruct/Decompose
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a : Bool ⊢ Π b : Bool, ?M::0 ⇒ ?M::1 ≺ Π b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
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Destruct/Decompose
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⊢ Π a b : Bool, ?M::0 ⇒ ?M::1 ≺ Π a b : Bool, ((a ⇒ b) ⇒ a) ⇒ a
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(line: 26: pos: 16) Type of definition 'pierce' must be convertible to expected type.
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