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

  Set: pp::colors
  Set: pp::unicode
  Assumed: A
  Assumed: B
  Assumed: A'
  Assumed: B'
  Assumed: H
  Assumed: a
DomInj H : A == A'
  Proved: BeqB'
  Set: lean::pp::implicit
DomInj::explicit A A' (λ x : A, B) (λ x : A', B') H
RanInj::explicit 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> 2013-09-07 01:31:47 +00:00			`Set: pp::colors`
			`Set: pp::unicode`
			`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 23:20:02 +00:00			`DomInj H : A == A'`
Add Cast, DomInj and RanInj. Improve operator << for lean_frontend objects. Signed-off-by: Leonardo de Moura <leonardo@microsoft.com> 2013-09-07 01:31:47 +00:00			`Proved: BeqB'`
			`Set: lean::pp::implicit`
			`DomInj::explicit A A' (λ x : A, B) (λ x : A', B') H`
			`RanInj::explicit A A' (λ x : A, B) (λ x : A', B') H a`