%   ORIGINAL: 'h4/thm/arithmetic/MULT_EQ_1_'
% 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 y. 'h4/const/arithmetic/*' x y = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO') <=> x = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO') /\ y = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')
%   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 y. 'h4/const/arithmetic/*' x y = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO') <=> x = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO') /\ y = 'h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO')
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_3f80091,V_3f80087]: ![F, G]: (![X]: s(V_3f80087,happ(s(fun(V_3f80091,V_3f80087),F),s(V_3f80091,X))) = s(V_3f80087,happ(s(fun(V_3f80091,V_3f80087),G),s(V_3f80091,X))) => s(fun(V_3f80091,V_3f80087),F) = s(fun(V_3f80091,V_3f80087),G))).
fof('h4/thm/arithmetic/MULT_EQ_1_', conjecture, ![X, Y]: (s('h4/type/num/num','h4/const/arithmetic/*'(s('h4/type/num/num',X),s('h4/type/num/num',Y))) = 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',X) = 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',Y) = 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')))))))).
