%   ORIGINAL: 'h4/thm/integral/DSIZE_EQ_'
% 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 D. 'h4/const/transc/division' ('h4/const/pair/,' a b) D ==> 'h4/const/real/real_sub' ('h4/const/real/sum' ('h4/const/pair/,' 'h4/const/num/0' ('h4/const/transc/dsize' D)) (\n. 'h4/const/real/real_sub' (D ('h4/const/num/SUC' n)) (D n))) ('h4/const/real/real_sub' b a) = '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. (!D n. happ (happ _0 D) n = 'h4/const/real/real_sub' (happ D ('h4/const/num/SUC' n)) (happ D n)) ==> (!a b D. 'h4/const/transc/division' ('h4/const/pair/,' a b) D ==> 'h4/const/real/real_sub' ('h4/const/real/sum' ('h4/const/pair/,' 'h4/const/num/0' ('h4/const/transc/dsize' D)) (happ _0 D)) ('h4/const/real/real_sub' b 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_3f39631,V_3f39627]: ![F, G]: (![X]: s(V_3f39627,happ(s(fun(V_3f39631,V_3f39627),F),s(V_3f39631,X))) = s(V_3f39627,happ(s(fun(V_3f39631,V_3f39627),G),s(V_3f39631,X))) => s(fun(V_3f39631,V_3f39627),F) = s(fun(V_3f39631,V_3f39627),G))).
fof('h4/thm/integral/DSIZE_EQ_', conjecture, ![V__0]: (![D, N]: s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),D))),s('h4/type/num/num',N))) = s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num','h4/const/num/SUC'(s('h4/type/num/num',N))))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num',N))))) => ![A, B, D]: (p(s(bool,'h4/const/transc/division'(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/num/num','h4/type/realax/real'),D)))) => s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real','h4/const/real/sum'(s('h4/type/pair/prod'('h4/type/num/num','h4/type/num/num'),'h4/const/pair/,'(s('h4/type/num/num','h4/const/num/0'),s('h4/type/num/num','h4/const/transc/dsize'(s(fun('h4/type/num/num','h4/type/realax/real'),D))))),s(fun('h4/type/num/num','h4/type/realax/real'),happ(s(fun(fun('h4/type/num/num','h4/type/realax/real'),fun('h4/type/num/num','h4/type/realax/real')),V__0),s(fun('h4/type/num/num','h4/type/realax/real'),D))))),s('h4/type/realax/real','h4/const/real/real_sub'(s('h4/type/realax/real',B),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')))))).
