%   ORIGINAL: 'h4/thm/prim_rec/SIMP_REC_REL_UNIQUE_'
% 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: !x f g1 g2 m1 m2. 'h4/const/prim_rec/SIMP_REC_REL' g1 x f m1 /\ 'h4/const/prim_rec/SIMP_REC_REL' g2 x f m2 ==> (!n. 'h4/const/prim_rec/<' n m1 /\ 'h4/const/prim_rec/<' n m2 ==> g1 n = g2 n)
%   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: !x f g1 g2 m1 m2. 'h4/const/prim_rec/SIMP_REC_REL' g1 x f m1 /\ 'h4/const/prim_rec/SIMP_REC_REL' g2 x f m2 ==> (!n. 'h4/const/prim_rec/<' n m1 /\ 'h4/const/prim_rec/<' n m2 ==> happ g1 n = happ g2 n)
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_3f86744,V_3f86740]: ![F, G]: (![X]: s(V_3f86740,happ(s(fun(V_3f86744,V_3f86740),F),s(V_3f86744,X))) = s(V_3f86740,happ(s(fun(V_3f86744,V_3f86740),G),s(V_3f86744,X))) => s(fun(V_3f86744,V_3f86740),F) = s(fun(V_3f86744,V_3f86740),G))).
fof('h4/thm/prim_rec/SIMP_REC_REL_UNIQUE_', conjecture, ![A]: ![X, F, G1, G2, M1, M2]: ((p(s(bool,'h4/const/prim_rec/SIMP_REC_REL'(s(fun('h4/type/num/num',A),G1),s(A,X),s(fun(A,A),F),s('h4/type/num/num',M1)))) & p(s(bool,'h4/const/prim_rec/SIMP_REC_REL'(s(fun('h4/type/num/num',A),G2),s(A,X),s(fun(A,A),F),s('h4/type/num/num',M2))))) => ![N]: ((p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N),s('h4/type/num/num',M1)))) & p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',N),s('h4/type/num/num',M2))))) => s(A,happ(s(fun('h4/type/num/num',A),G1),s('h4/type/num/num',N))) = s(A,happ(s(fun('h4/type/num/num',A),G2),s('h4/type/num/num',N)))))).
