lean4-htt/tests/lean/elab9.lean.expected.out
Leonardo de Moura 5cef84709f refactor(library): avoid auxiliary definitions such as add/mul/le/etc
See Section "Other goodies" at
https://github.com/leanprover/lean/wiki/Refactoring-structures

This commit also improves the support for projections in the
unifier/matcher.

Now, we consider the extra case-split for projections.
Given a projection `proj`, and the constraint `proj s =?= proj t`, we need to try first `s =?= t` and if it fails, then try to reduce.
This is needed in the standard library because we now have constraints such as:
```
@has_le.le ?A ?s ?a ?b  =?=  @has_le.le nat nat.has_add x y
```
If we reduce the right hand side, we get the unsolvable constraint
```
@has_le.le ?A ?s ?a ?b  =?=  nat.le x y
```
Before this change, the constraint was `@le ?A ?s ?a ?b  =?=  @le nat nat.has_add x y`, and we already perform a case-split in this case.
Moreover, projections were eagerly reduced whenever possible.
The extra case-split generates a performance problem in several tests. For example `fib 8 = 34` was timing out.
I worked around this issue by performing the case-split only when the constraint contains meta-variables.
There are also minor issues. Example. `<` is notation for `has_lt.lt`, but `>` is for `gt`.
2017-05-01 08:52:19 -07:00

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λ (A : Type u_1) [_inst_1 : has_add A] [_inst_2 : has_zero A] (a : A)
(H : @eq A (@has_add.add A _inst_1 a (@has_zero.zero A _inst_2)) a) [_inst_3 : has_add A]
(H : @eq A a (@has_add.add A _inst_3 (@has_zero.zero A _inst_2) (@has_zero.zero A _inst_2))),
@has_add.add A _inst_3 a a :
Π (A : Type u_1) [_inst_1 : has_add A] [_inst_2 : has_zero A] (a : A),
@eq A (@has_add.add A _inst_1 a (@has_zero.zero A _inst_2)) a →
Π [_inst_3 : has_add A],
@eq A a (@has_add.add A _inst_3 (@has_zero.zero A _inst_2) (@has_zero.zero A _inst_2)) → A
λ (a b : nat) (H : @gt nat nat.has_lt a b) [_inst_1 : has_lt nat], @has_lt.lt nat _inst_1 a b :
Π (a b : nat), @gt nat nat.has_lt a b → Π [_inst_1 : has_lt nat], Prop