%   ORIGINAL: 'h4/thm/integral/DINT_DELTA_LEFT_'
% 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: !a b. 'h4/const/transc/Dint' ('h4/const/pair/,' a b) (\x. 'h4/const/bool/COND' (x = a) ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ('h4/const/real/real_of_num' 'h4/const/num/0')) ('h4/const/real/real_of_num' '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: !_0. (!a x. ?v. (v <=> x = a) /\ happ (happ _0 a) x = 'h4/const/bool/COND' v ('h4/const/real/real_of_num' ('h4/const/arithmetic/NUMERAL' ('h4/const/arithmetic/BIT1' 'h4/const/arithmetic/ZERO'))) ('h4/const/real/real_of_num' 'h4/const/num/0')) ==> (!a b. 'h4/const/transc/Dint' ('h4/const/pair/,' a b) (happ _0 a) ('h4/const/real/real_of_num' '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_3f40406,V_3f40402]: ![F, G]: (![X]: s(V_3f40402,happ(s(fun(V_3f40406,V_3f40402),F),s(V_3f40406,X))) = s(V_3f40402,happ(s(fun(V_3f40406,V_3f40402),G),s(V_3f40406,X))) => s(fun(V_3f40406,V_3f40402),F) = s(fun(V_3f40406,V_3f40402),G))).
fof('h4/thm/integral/DINT_DELTA_LEFT_', conjecture, ![V__0]: (![A, X]: ?[V]: ((p(s(bool,V)) <=> s('h4/type/realax/real',X) = s('h4/type/realax/real',A)) & s('h4/type/realax/real',happ(s(fun('h4/type/realax/real','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real','h4/type/realax/real')),V__0),s('h4/type/realax/real',A))),s('h4/type/realax/real',X))) = s('h4/type/realax/real','h4/const/bool/COND'(s(bool,V),s('h4/type/realax/real','h4/const/real/real_of_num'(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/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))))) => ![A, B]: p(s(bool,'h4/const/transc/Dint'(s('h4/type/pair/prod'('h4/type/realax/real','h4/type/realax/real'),'h4/const/pair/,'(s('h4/type/realax/real',A),s('h4/type/realax/real',B))),s(fun('h4/type/realax/real','h4/type/realax/real'),happ(s(fun('h4/type/realax/real',fun('h4/type/realax/real','h4/type/realax/real')),V__0),s('h4/type/realax/real',A))),s('h4/type/realax/real','h4/const/real/real_of_num'(s('h4/type/num/num','h4/const/num/0')))))))).
