rewrite

rewrite takes an equivalence proof as input, like t1 = t2, and replaces all occurances of t1 with t2. Replacement of t2 with t1 can be achieved with the variant rewrite <- (rewrite backwards). Multiple rewrites can be chained with one tactic via a list of comma-separated equivalence proofs. Each of the equivalence proofs in the chain may be rewritten backwards. rewrite will fail if there are no t1’s (in this example) to replace.

Syntax

(* Replace t1 with t2 in the goal *)
rewrite t1_eq_t2.

(* Rewrite in an assumption *)
rewrite Eq in H.

(* Rewrite in the goal and all assumptions *)
rewrite HEq in *.

(* Rewrite multiple values *)
rewrite t1_eq_t2, <- x_eq_y, ht_eq_ht.

Examples

Before

x, y: nat
H: x = y
=========================
x + y = y + y

rewrite H.

After

x, y: nat
H: x = y
=========================
y + y = y + y

Alternatively,

rewrite <- H.

x, y: nat
H: x = y
=========================
x + x = x + x

Resources

Reference Documentation

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