lean2/tests/lean/elab7.lean.expected.out

  Set: pp::colors
  Set: pp::unicode
  Assumed: A
  Assumed: B
  Assumed: C
  Assumed: P
  Assumed: F1
  Assumed: F2
  Assumed: H
  Assumed: a
eta (F2 a) : (λ x : B, F2 a x) = F2 a
funext (λ a : A, trans (symm (eta (F1 a))) (trans (funext (λ b : B, H a b)) (eta (F2 a)))) :
    (λ x : A, F1 x) = (λ x : A, F2 x)
funext (λ a : A, funext (λ b : B, H a b)) : (λ (x : A) (x::1 : B), F1 x x::1) = (λ (x : A) (x::1 : B), F2 x x::1)
  Proved: T1
  Proved: T2
  Proved: T3
  Proved: T4
theorem T1 : F1 = F2 := funext (λ a : A, funext (λ b : B, H a b))
theorem T2 : (λ (x1 : A) (x2 : B), F1 x1 x2) = F2 := funext (λ a : A, funext (λ b : B, H a b))
theorem T3 : F1 = (λ (x1 : A) (x2 : B), F2 x1 x2) := funext (λ a : A, funext (λ b : B, H a b))
theorem T4 : (λ (x1 : A) (x2 : B), F1 x1 x2) = (λ (x1 : A) (x2 : B), F2 x1 x2) :=
    funext (λ a : A, funext (λ b : B, H a b))
  Set: lean::pp::implicit
theorem T1 : @eq (A → B → C) F1 F2 :=
    @funext A (λ x : A, B → C) F1 F2 (λ a : A, @funext B (λ x : B, C) (F1 a) (F2 a) (λ b : B, H a b))
theorem T2 : @eq (A → B → C) (λ (x1 : A) (x2 : B), F1 x1 x2) F2 :=
    @funext A
            (λ x : A, B → C)
            (λ (x1 : A) (x2 : B), F1 x1 x2)
            F2
            (λ a : A, @funext B (λ x : B, C) (λ x2 : B, F1 a x2) (F2 a) (λ b : B, H a b))
theorem T3 : @eq (A → B → C) F1 (λ (x1 : A) (x2 : B), F2 x1 x2) :=
    @funext A
            (λ x : A, B → C)
            F1
            (λ (x1 : A) (x2 : B), F2 x1 x2)
            (λ a : A, @funext B (λ x : B, C) (F1 a) (λ x2 : B, F2 a x2) (λ b : B, H a b))
theorem T4 : @eq (A → B → C) (λ (x1 : A) (x2 : B), F1 x1 x2) (λ (x1 : A) (x2 : B), F2 x1 x2) :=
    @funext A
            (λ x : A, B → C)
            (λ (x1 : A) (x2 : B), F1 x1 x2)
            (λ (x1 : A) (x2 : B), F2 x1 x2)
            (λ a : A, @funext B (λ x : B, C) (λ x2 : B, F1 a x2) (λ x2 : B, F2 a x2) (λ b : B, H a b))
test(tests/lean): new elaborator tests Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-16 06:00:26 +00:00			`Set: pp::colors`
			`Set: pp::unicode`
			`Assumed: A`
			`Assumed: B`
			`Assumed: C`
			`Assumed: P`
			`Assumed: F1`
			`Assumed: F2`
			`Assumed: H`
			`Assumed: a`
fix(tests/lean): adjust tests to reflect recent changes Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-16 00:35:33 +00:00			`eta (F2 a) : (λ x : B, F2 a x) = F2 a`
chore(builtin/kernel): remove \bowtie as notation for transitivity Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-19 05:11:12 +00:00			`funext (λ a : A, trans (symm (eta (F1 a))) (trans (funext (λ b : B, H a b)) (eta (F2 a)))) :`
			`(λ x : A, F1 x) = (λ x : A, F2 x)`
refactor(kernel): remove heterogeneous equality Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-16 23:07:51 +00:00			`funext (λ a : A, funext (λ b : B, H a b)) : (λ (x : A) (x::1 : B), F1 x x::1) = (λ (x : A) (x::1 : B), F2 x x::1)`
test(tests/lean): new elaborator tests Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-16 06:00:26 +00:00			`Proved: T1`
			`Proved: T2`
			`Proved: T3`
			`Proved: T4`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`theorem T1 : F1 = F2 := funext (λ a : A, funext (λ b : B, H a b))`
			`theorem T2 : (λ (x1 : A) (x2 : B), F1 x1 x2) = F2 := funext (λ a : A, funext (λ b : B, H a b))`
			`theorem T3 : F1 = (λ (x1 : A) (x2 : B), F2 x1 x2) := funext (λ a : A, funext (λ b : B, H a b))`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem T4 : (λ (x1 : A) (x2 : B), F1 x1 x2) = (λ (x1 : A) (x2 : B), F2 x1 x2) :=`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`funext (λ a : A, funext (λ b : B, H a b))`
test(tests/lean): new elaborator tests Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-16 06:00:26 +00:00			`Set: lean::pp::implicit`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem T1 : @eq (A → B → C) F1 F2 :=`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`@funext A (λ x : A, B → C) F1 F2 (λ a : A, @funext B (λ x : B, C) (F1 a) (F2 a) (λ b : B, H a b))`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem T2 : @eq (A → B → C) (λ (x1 : A) (x2 : B), F1 x1 x2) F2 :=`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`@funext A`
			`(λ x : A, B → C)`
			`(λ (x1 : A) (x2 : B), F1 x1 x2)`
			`F2`
			`(λ a : A, @funext B (λ x : B, C) (λ x2 : B, F1 a x2) (F2 a) (λ b : B, H a b))`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem T3 : @eq (A → B → C) F1 (λ (x1 : A) (x2 : B), F2 x1 x2) :=`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`@funext A`
			`(λ x : A, B → C)`
			`F1`
			`(λ (x1 : A) (x2 : B), F2 x1 x2)`
			`(λ a : A, @funext B (λ x : B, C) (F1 a) (λ x2 : B, F2 a x2) (λ b : B, H a b))`
feat(frontends/lean): use lowercase commands, replace 'endscope' and 'endnamespace' with 'end' Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-05 20:05:08 +00:00			`theorem T4 : @eq (A → B → C) (λ (x1 : A) (x2 : B), F1 x1 x2) (λ (x1 : A) (x2 : B), F2 x1 x2) :=`
refactor(builtin/kernel): prove eta using function extensionality, and rename abst and abstpi to funext and allext Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2014-01-09 01:25:14 +00:00			`@funext A`
			`(λ x : A, B → C)`
			`(λ (x1 : A) (x2 : B), F1 x1 x2)`
			`(λ (x1 : A) (x2 : B), F2 x1 x2)`
			`(λ a : A, @funext B (λ x : B, C) (λ x2 : B, F1 a x2) (λ x2 : B, F2 a x2) (λ b : B, H a b))`