lean2/tests/lean/tst11.lean.expected.out
Leonardo de Moura 4dd6cead83 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 16:20:06 -07:00

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Set: pp::colors
Set: pp::unicode
Defined: xor
⊕ ⊥
Assumed: a
a ⊕ a ⊕ a
Subst::explicit : Π (A : Type U) (a b : A) (P : A → Bool), (P a) → (a == b) → (P b)
Proved: EM2
EM2 : Π a : Bool, a ¬ a
EM2 a : a ¬ a