%   ORIGINAL: 'h4/thm/prim_rec/PRIM_REC_EQN_0'
% 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 n. 'h4/const/prim_rec/PRIM_REC_FUN' x f 'h4/const/num/0' n = x
%   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 n. 'h4/const/prim_rec/PRIM_REC_FUN' x f 'h4/const/num/0' n = x
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_3f86944,V_3f86940]: ![F, G]: (![X]: s(V_3f86940,happ(s(fun(V_3f86944,V_3f86940),F),s(V_3f86944,X))) = s(V_3f86940,happ(s(fun(V_3f86944,V_3f86940),G),s(V_3f86944,X))) => s(fun(V_3f86944,V_3f86940),F) = s(fun(V_3f86944,V_3f86940),G))).
fof('h4/thm/prim_rec/PRIM_REC_EQN_0', conjecture, ![A]: ![X, F, N]: s(A,'h4/const/prim_rec/PRIM_REC_FUN'(s(A,X),s(fun(A,fun('h4/type/num/num',A)),F),s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num',N))) = s(A,X)).
