# Setoid Re Write A Sentence

The toolbox also extends the automatic rewriting capabilities of the system, allowing This documentation is adapted from the previous setoid documentation by. But, in the meantime, let me try to explain how it is possible to rewrite a term in a To illustrate my statement, we will consider the following definition of a gate in Coq: . calgarydanceteacherexpo.com module first, in order to have the Add Parametric Relation .

## DISCRIMINATE TACTIC COQ

For discriminate to work, the terms must be "structurally" different. This means that both terms are elements of an inductive set but. dependent inversion · dependent inversion with dependent rewrite -> · dependent rewrite discriminate · discrR · do.

### INTUITION TACTIC COQ

The intuition tactic also intros variables and hypotheses and applies tactics to them, including auto. Sometimes it works when auto. induction · induction using info_trivial · injection · instantiate · intro · intros · intros intuition · inversion · inversion_clear · inversion_sigma · is_evar · is_var.

## APPLY LEMMA TO HYPOTHESIS COQ

We can apply that hypothesis to a goal of y to transform it into x. In this Lemma modus_ponens: forall p q: Prop, (p -> q) -> p -> q. You can use pose proof theorem_name as X., where X is the name you want to introduce. If you're going to destruct it right away, you can also.

## REWRITE HYPOTHESIS

This is not as elegant as just an apply, but you can use pose proof (lemma _ _ H) as H0, where lemma is the name of your lemma. This will. Your hypothesis IHl1 is: IHl1: forall (Y: Type) (l2: list Y), length l1 = length l2 -> split (combine l1 l2) = (l1, l2). So in order to rewrite it, you need.

### DEPENDENT INDUCTION COQ

You can do. Require Import calgarydanceteacherexpo.comty. Lemma le_minus: forall n:nat , n n = 0. Proof. intros n H. remember 1 as m in H. The tactics dependent induction and dependent destruction are another solution for inverting inductive predicate instances and potentially doing induction at the.

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