Cong

simpLib.Cong : thm -> thm

Marks a theorem as a congruence rule for the simplifier.

The Cong function marks (or “tags”) a theorem so that when passed to the simplifier, it is not used as a rewrite, but rather as a congruence rule. This is a simpler way of adding a congruence rule to the simplifier than using the underlying SSFRAG function.

Failure

Never fails. On the other hand, Cong does not check that the theorem passed as an argument is a valid congruence rule, and invalid congruence rules may have unpredictable effects on the behaviour of the simplifier.

Example

   - SIMP_CONV pure_ss [] ``!x::P. x IN P /\ Q x``;
   <<HOL message: inventing new type variable names: 'a>>
   ! Uncaught exception:
   ! UNCHANGED
   - RES_FORALL_CONG;
   > val it =
       |- (P = Q) ==>
          (!x. x IN Q ==> (f x = g x)) ==>
          (RES_FORALL P f = RES_FORALL Q g) : thm
   - SIMP_CONV pure_ss [Cong RES_FORALL_CONG] ``!x::P. x IN P ``;
   <<HOL message: inventing new type variable names: 'a>>
   > val it = |- (!x::P. x IN P /\ Q x) = !x::P. T /\ Q x : thm

(Note that RES_FORALL_CONG is already included in bool_ss and all simpsets built on it.)

See also

simpLib.SSFRAG