%   ORIGINAL: 'h4/thm/arithmetic/X_LT_EXP_X_IFF_'
% 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 b. 'h4/const/prim_rec/<' x ('h4/const/arithmetic/EXP' b x) <=> 'h4/const/prim_rec/<' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')) b \/ x = 'h4/const/num/0'
%   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 b. 'h4/const/prim_rec/<' x ('h4/const/arithmetic/EXP' b x) <=> 'h4/const/prim_rec/<' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')) b \/ x = 'h4/const/num/0'
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_3f83692,V_3f83688]: ![F, G]: (![X]: s(V_3f83688,happ(s(fun(V_3f83692,V_3f83688),F),s(V_3f83692,X))) = s(V_3f83688,happ(s(fun(V_3f83692,V_3f83688),G),s(V_3f83692,X))) => s(fun(V_3f83692,V_3f83688),F) = s(fun(V_3f83692,V_3f83688),G))).
fof('h4/thm/arithmetic/X_LT_EXP_X_IFF_', conjecture, ![X, B]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',X),s('h4/type/num/num','h4/const/arithmetic/EXP'(s('h4/type/num/num',B),s('h4/type/num/num',X)))))) <=> (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num','h4/const/arithmetic/NUMERAL'(s('h4/type/num/num','h4/const/arithmetic/BIT1'(s('h4/type/num/num','h4/const/arithmetic/ZERO'))))),s('h4/type/num/num',B)))) | s('h4/type/num/num',X) = s('h4/type/num/num','h4/const/num/0')))).
