lean2/tests/lean/cast2.lean.expected.out

  Set: pp::colors
  Set: pp::unicode
  Assumed: cast
  Assumed: CastEq
  Assumed: CastApp
  Assumed: DomInj
  Assumed: RanInj
  Assumed: A
  Assumed: B
  Assumed: A'
  Assumed: B'
  Assumed: H
  Assumed: a
DomInj H : A == A'
  Proved: BeqB'
  Set: lean::pp::implicit
@DomInj A A' (λ x : A, B) (λ x : A', B') H
@RanInj A A' (λ x : A, B) (λ x : A', B') H a
Add Cast, DomInj and RanInj. Improve operator << for lean_frontend objects. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-06 18:31:47 -07:00			`Set: pp::colors`
			`Set: pp::unicode`
refactor(library/cast): use .lean file instead of .cpp file to define casting library Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-23 22:04:19 -08:00			`Assumed: cast`
			`Assumed: CastEq`
			`Assumed: CastApp`
			`Assumed: DomInj`
			`Assumed: RanInj`
Add Cast, DomInj and RanInj. Improve operator << for lean_frontend objects. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-06 18:31:47 -07:00			`Assumed: A`
			`Assumed: B`
			`Assumed: A'`
			`Assumed: B'`
			`Assumed: H`
			`Assumed: a`
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 16:20:02 -07:00			`DomInj H : A == A'`
Add Cast, DomInj and RanInj. Improve operator << for lean_frontend objects. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-06 18:31:47 -07:00			`Proved: BeqB'`
			`Set: lean::pp::implicit`
feat(frontends/lean): simplify explicit version names Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-12-21 17:02:16 -08:00			`@DomInj A A' (λ x : A, B) (λ x : A', B') H`
			`@RanInj A A' (λ x : A, B) (λ x : A', B') H a`