This modification was suggested by @kha.
TODO:
- Use `simp [-f]` instead of `simp without f`
- Allow users to remove hypothesis from `*`. Example: `simp [*, -h]`
for simplify using all hypotheses but `h`.
Before this commit, the `by_cases p` tactic would synthesize
`inst : decidable p` type class resolution, and then use the
`cases` tactic (dependent elimination). This would create
problems since occurrences of `inst` would be replaced with
`decidable.is_true h` in one branch, and `decidable.is_false h` in the
other. Where `h`s (we have two of them, one for each branch) are
fresh hypotheses introduced by the `cases` tactic.
For example, assume we have the term in our goal.
`@ite p inst A a b`
This term would become
`@ite p (decidable.is_true h) A a b` (in the first branch where `h : p`)
and
`@ite p (decidable.is_false h) A a b` (in the second where `h : not p`)
Now, suppose we try to executed the following tactic in the first branch
`rw [if_pos h]`
it will fail since `if_pos h` is actually `@if_pos p inst h`, and
we will not be able to unify
`@ite p (decidable.is_true h) A a b =?= @ite p inst ?A ?a ?b`
This commit workarounds this problem by applying cases on
`@decidable.em p inst : p or not p` instead of `inst : decidable p`.
Thus, the term `inst` is not replaced with `decidable.is_true h` and
`decidable.is_false h`.
The new test `tests/lean/run/simp_dif.lean` demonstrates the problem above.
See issue #1694.
There is an orthogonal issue. `simp` (and consequently `unfold`) cannot be used to
reduce projections (e.g., `has_add.add`). This issue has been
previously raised by @Armael, but it was not addressed yet.
closes#1675
After this commit, the following example works as expected.
```
example (p : nat → Prop) (a b : nat) : a = 0 ∧ b = 0 → p (a + b) → p 0 :=
begin
intros h₁ h₂,
simp [h₁] at *,
/- produces the state
(p : nat → Prop) (a b : nat)
h₁ : true
h₂ : p 0
|- p 0
-/
assumption
end
```
as expected.
Remark: the original issue raised by issue #1675 is actually solved by the
`simp_all` tactic.
The type-correctness of binary_rec_eq (the statement, not the proof) depends on unfolding the embedded well-founded definition of mod. This definition avoids it by using two simpler functions bodd and div2 that reduce well in the kernel.
See issue #1175
BTW, we may have to revise this decision in the future when we decide to
populate the string library with lemmas.
It is inconvenient to prove the lemmas at string/basic.lean since the
tactic framework has not been defined yet.
Anyway, I think it is worth to keep the private for now, and make sure
nobody relies on its implementation.
We want to make sure string users do not depend on the string
implementation. This is the first step.
We need this refactoring *now* to make sure it will not be
super painful to address issue #1175
replace_target uses id_locked.
The id_locked solution is more robust because simp may build a proof
using refl lemmas, but type_context may not be able to establish that
the previous and new target are definitionally equal.
@Armael This commit fixes the issue in the KreMLin proof you showed me.
Now, the following tactic succeeds (as expected)
```
simp [lowstar_semantics.apply_ectx],
```
and the resulting goal is
```
...
|- exp.subbuf (exp.loc (b, n, list.nil field)) a_1 = exp.subbuf ↑?m_1 ?m_2
```
(1) The lhs and rhs will be reduced to whnf before getting the constructor apps
(2) If the lhs and rhs are distinct constructors, it discharges the goal by contradiction
(3) The interactive injection tactic will try to close the goal by assumption if successful
