375 lines
15 KiB
Text
375 lines
15 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
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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
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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
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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
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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
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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
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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) invalid expression, it still contains metavariables after elaboration, metavariable: ?M::1, type:
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Type
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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
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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
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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
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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
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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
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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
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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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⊢ (?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?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
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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 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 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 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 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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⊢ (?M::0 ≈ Type) ⊕ (?M::0 ≈ (Type 1)) ⊕ (?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
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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 6
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 5
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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 7
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 5
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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 8
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 5
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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 9
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Assignment
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⊢ ?M::1 ≈ Bool
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Assumption 5
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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
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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
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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
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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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