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prove_abs_fn_onto                                              (Drule)
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prove_abs_fn_onto : thm -> thm

SYNOPSIS
Proves that a type abstraction function is onto (surjective).

DESCRIBE
If {th} is a theorem of the form returned by the function
{define_new_type_bijections}:

   |- (!a. abs(rep a) = a) /\ (!r. P r = (rep(abs r) = r))

then {prove_abs_fn_onto th} proves from this theorem that the
function {abs} is onto, returning the theorem:

   |- !a. ?r. (a = abs r) /\ P r




FAILURE
Fails if applied to a theorem not of the form shown above.

SEEALSO
Definition.new_type_definition, Drule.define_new_type_bijections,
Drule.prove_abs_fn_one_one, Drule.prove_rep_fn_one_one,
Drule.prove_rep_fn_onto.

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