lean2/tests/lean/tst4.lean.expected.out

  Set: pp::colors
  Set: pp::unicode
  Assumed: f
  Assumed: N
  Assumed: n1
  Assumed: n2
  Set: lean::pp::implicit
f::explicit N n1 n2
f::explicit ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)
  Assumed: EqNice
EqNice::explicit N n1 n2
f::explicit N n1 n2 : N
Congr::explicit :
    Π (A : Type U) (B : A → (Type U)) (f g : Π x : A, B x) (a b : A), f == g → a == b → (f a) == (g b)
f::explicit N n1 n2
  Assumed: a
  Assumed: b
  Assumed: c
  Assumed: g
  Assumed: H1
  Proved: Pr
Axiom H1 : eq::explicit N a b ∧ eq::explicit N b c
Theorem Pr : eq::explicit N (g a) (g c) :=
    Congr::explicit
        N
        (λ x : N, N)
        g
        g
        a
        c
        (Refl::explicit (N → N) g)
        (Trans::explicit
             N
             a
             b
             c
             (Conjunct1::explicit (eq::explicit N a b) (eq::explicit N b c) H1)
             (Conjunct2::explicit (eq::explicit N a b) (eq::explicit N b c) H1))
Fix unit tests for Windows Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-03 17:44:51 +00:00			`Set: pp::colors`
			`Set: pp::unicode`
Move files in examples directory to tests directory. They are not real examples Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-01 02:15:48 +00:00			`Assumed: f`
			`Assumed: N`
			`Assumed: n1`
			`Assumed: n2`
Modify verbose message for Set command Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-02 19:29:21 +00:00			`Set: lean::pp::implicit`
Move files in examples directory to tests directory. They are not real examples Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-01 02:15:48 +00:00			`f::explicit N n1 n2`
Fix unit tests for Windows Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-03 17:44:51 +00:00			`f::explicit ((N → N) → N → N) (λ x : N → N, x) (λ y : N → N, y)`
Move files in examples directory to tests directory. They are not real examples Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-01 02:15:48 +00:00			`Assumed: EqNice`
			`EqNice::explicit N n1 n2`
Fix test error on Cygwin Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-10 01:35:11 +00:00			`f::explicit N n1 n2 : N`
Display the input term in the output of the Check command. It is useful to see the fully elaborated term. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-09 05:54:22 +00:00			`Congr::explicit :`
fix(frontends/lean/notation): change the precedence of '->' It should match the precedence of the implication '=>'. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-06 21:23:20 +00:00			`Π (A : Type U) (B : A → (Type U)) (f g : Π x : A, B x) (a b : A), f == g → a == b → (f a) == (g b)`
Move files in examples directory to tests directory. They are not real examples Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-01 02:15:48 +00:00			`f::explicit N n1 n2`
			`Assumed: a`
			`Assumed: b`
			`Assumed: c`
			`Assumed: g`
			`Assumed: H1`
			`Proved: Pr`
refactor(equality): make homogeneous equality the default equality It was not a good idea to use heterogeneous equality as the default equality in Lean. It creates the following problems. - Heterogeneous equality does not propagate constraints in the elaborator. For example, suppose that l has type (List Int), then the expression l = nil will not propagate the type (List Int) to nil. - It is easy to write false. For example, suppose x has type Real, and the user writes x = 0. This is equivalent to false, since 0 has type Nat. The elaborator cannot introduce the coercion since x = 0 is a type correct expression. Homogeneous equality does not suffer from the problems above. We keep heterogeneous equality because it is useful for generating proof terms. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-10-29 23:20:02 +00:00			`Axiom H1 : eq::explicit N a b ∧ eq::explicit N b c`
			`Theorem Pr : eq::explicit N (g a) (g c) :=`
fix(tests/lean): adjust tests Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-10-24 22:42:17 +00:00			`Congr::explicit`
			`N`
			`(λ x : N, N)`
			`g`
			`g`
			`a`
			`c`
			`(Refl::explicit (N → N) g)`
refactor(equality): make homogeneous equality the default equality It was not a good idea to use heterogeneous equality as the default equality in Lean. It creates the following problems. - Heterogeneous equality does not propagate constraints in the elaborator. For example, suppose that l has type (List Int), then the expression l = nil will not propagate the type (List Int) to nil. - It is easy to write false. For example, suppose x has type Real, and the user writes x = 0. This is equivalent to false, since 0 has type Nat. The elaborator cannot introduce the coercion since x = 0 is a type correct expression. Homogeneous equality does not suffer from the problems above. We keep heterogeneous equality because it is useful for generating proof terms. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-10-29 23:20:02 +00:00			`(Trans::explicit`
			`N`
			`a`
			`b`
			`c`
			`(Conjunct1::explicit (eq::explicit N a b) (eq::explicit N b c) H1)`
			`(Conjunct2::explicit (eq::explicit N a b) (eq::explicit N b c) H1))`