# The `simp_rw`

tactic #

This file defines the `simp_rw`

tactic: it functions as a mix of `simp`

and `rw`

.
Like `rw`

, it applies each rewrite rule in the given order, but like `simp`

it repeatedly applies
these rules and also under binders like `∀ x, ...`

, `∃ x, ...`

and `fun x ↦ ...`

.

def
Mathlib.Tactic.withSimpRWRulesSeq
(token : Lean.Syntax)
(rwRulesSeqStx : Lean.Syntax)
(x : Bool → Lean.Syntax → Lean.Elab.Tactic.TacticM Unit)
:

A version of `withRWRulesSeq`

(in core) that doesn't attempt to find equation lemmas, and simply
passes the rw rules on to `x`

.

## Equations

- One or more equations did not get rendered due to their size.

## Instances For

`simp_rw`

functions as a mix of `simp`

and `rw`

. Like `rw`

, it applies each
rewrite rule in the given order, but like `simp`

it repeatedly applies these
rules and also under binders like `∀ x, ...`

, `∃ x, ...`

and `fun x ↦...`

.
Usage:

`simp_rw [lemma_1, ..., lemma_n]`

will rewrite the goal by applying the lemmas in that order. A lemma preceded by`←`

is applied in the reverse direction.`simp_rw [lemma_1, ..., lemma_n] at h₁ ... hₙ`

will rewrite the given hypotheses.`simp_rw [...] at *`

rewrites in the whole context: all hypotheses and the goal.

Lemmas passed to `simp_rw`

must be expressions that are valid arguments to `simp`

.
For example, neither `simp`

nor `rw`

can solve the following, but `simp_rw`

can:

```
example {a : ℕ}
(h1 : ∀ a b : ℕ, a - 1 ≤ b ↔ a ≤ b + 1)
(h2 : ∀ a b : ℕ, a ≤ b ↔ ∀ c, c < a → c < b) :
(∀ b, a - 1 ≤ b) = ∀ b c : ℕ, c < a → c < b + 1 := by
simp_rw [h1, h2]
```

## Equations

- One or more equations did not get rendered due to their size.