%   ORIGINAL: 'h4/thm/prim_rec/measure_thm_'
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Goal: !f x y. 'h4/const/prim_rec/measure' f x y <=> 'h4/const/prim_rec/<' (f x) (f y)
%   PROCESSED
% Assm ['HL_TRUTH']: T
% Assm ['HL_FALSITY']: ~F
% Assm ['HL_BOOL_CASES']: !t. (t <=> T) \/ (t <=> F)
% Assm ['HL_EXT']: !f g. (!x. happ f x = happ g x) ==> f = g
% Goal: !f x y. 'h4/const/prim_rec/measure' f x y <=> 'h4/const/prim_rec/<' (happ f x) (happ f y)
fof('HL_TRUTH', axiom, p(s(bool,'T'))).
fof('HL_FALSITY', axiom, ~ (p(s(bool,'F')))).
fof('HL_BOOL_CASES', axiom, ![T]: (s(bool,T) = s(bool,'T') | s(bool,T) = s(bool,'F'))).
fof('HL_EXT', axiom, ![V_3f87219,V_3f87215]: ![F, G]: (![X]: s(V_3f87215,happ(s(fun(V_3f87219,V_3f87215),F),s(V_3f87219,X))) = s(V_3f87215,happ(s(fun(V_3f87219,V_3f87215),G),s(V_3f87219,X))) => s(fun(V_3f87219,V_3f87215),F) = s(fun(V_3f87219,V_3f87215),G))).
fof('h4/thm/prim_rec/measure_thm_', conjecture, ![A]: ![F, X, Y]: s(bool,'h4/const/prim_rec/measure'(s(fun(A,'h4/type/num/num'),F),s(A,X),s(A,Y))) = s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),F),s(A,X))),s('h4/type/num/num',happ(s(fun(A,'h4/type/num/num'),F),s(A,Y)))))).
