%   ORIGINAL: 'h4/thm/ind_type/NUMSUM_INJ_'
% 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: !b1 x1 b2 x2. 'h4/const/ind_type/NUMSUM' b1 x1 = 'h4/const/ind_type/NUMSUM' b2 x2 <=> (b1 <=> b2) /\ x1 = x2
%   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: !b1 x1 b2 x2. 'h4/const/ind_type/NUMSUM' b1 x1 = 'h4/const/ind_type/NUMSUM' b2 x2 <=> (b1 <=> b2) /\ x1 = x2
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_3f73864,V_3f73860]: ![F, G]: (![X]: s(V_3f73860,happ(s(fun(V_3f73864,V_3f73860),F),s(V_3f73864,X))) = s(V_3f73860,happ(s(fun(V_3f73864,V_3f73860),G),s(V_3f73864,X))) => s(fun(V_3f73864,V_3f73860),F) = s(fun(V_3f73864,V_3f73860),G))).
fof('h4/thm/ind_type/NUMSUM_INJ_', conjecture, ![B1, X1, B2, X2]: (s('h4/type/num/num','h4/const/ind_type/NUMSUM'(s(bool,B1),s('h4/type/num/num',X1))) = s('h4/type/num/num','h4/const/ind_type/NUMSUM'(s(bool,B2),s('h4/type/num/num',X2))) <=> (s(bool,B1) = s(bool,B2) & s('h4/type/num/num',X1) = s('h4/type/num/num',X2)))).
