lean4-htt/tests/lean/generalize1.lean
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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open tactic
add_key_equivalence has_add.add nat.succ
set_option pp.binder_types true
example (a b c : nat) : a + 1 = b + 1 → b + 1 = a + 1 :=
by do
a ← get_local `a, b ← get_local `b,
e₁ ← mk_app `nat.succ [a],
e₂ ← mk_app `nat.succ [b],
generalize e₁ `x,
generalize e₂ `y,
trace_state,
intros, symmetry, assumption