FUN_EQ_CONV

Conv.FUN_EQ_CONV : conv

Equates normal and extensional equality for two functions.

The conversion FUN_EQ_CONV embodies the fact that two functions are equal precisely when they give the same results for all values to which they can be applied. When supplied with a term argument of the form f = g, where f and g are functions of type ty1->ty2, FUN_EQ_CONV returns the theorem:

   |- (f = g) = (!x. f x = g x)

where x is a variable of type ty1 chosen by the conversion.

Failure

FUN_EQ_CONV tm fails if tm is not an equation f = g, where f and g are functions.

Used for proving equality of functions.

See also

Drule.EXT, Conv.X_FUN_EQ_CONV