%   ORIGINAL: 'h4/thm/integral/DIVISION_DSIZE_EQ_ALT_'
% 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 n. 'h4/const/transc/division' ('h4/const/pair/,' a b) d /\ d ('h4/const/num/SUC' n) = d n /\ (!i. 'h4/const/prim_rec/<' i n ==> 'h4/const/realax/real_lt' (d i) (d ('h4/const/num/SUC' i))) ==> 'h4/const/transc/dsize' d = n
%   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: !a b d n. 'h4/const/transc/division' ('h4/const/pair/,' a b) d /\ happ d ('h4/const/num/SUC' n) = happ d n /\ (!i. 'h4/const/prim_rec/<' i n ==> 'h4/const/realax/real_lt' (happ d i) (happ d ('h4/const/num/SUC' i))) ==> 'h4/const/transc/dsize' d = n
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_3f40281,V_3f40277]: ![F, G]: (![X]: s(V_3f40277,happ(s(fun(V_3f40281,V_3f40277),F),s(V_3f40281,X))) = s(V_3f40277,happ(s(fun(V_3f40281,V_3f40277),G),s(V_3f40281,X))) => s(fun(V_3f40281,V_3f40277),F) = s(fun(V_3f40281,V_3f40277),G))).
fof('h4/thm/integral/DIVISION_DSIZE_EQ_ALT_', conjecture, ![A, B, D, N]: ((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',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))) & ![I]: (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',I),s('h4/type/num/num',N)))) => p(s(bool,'h4/const/realax/real_lt'(s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num',I))),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',I))))))))))) => s('h4/type/num/num','h4/const/transc/dsize'(s(fun('h4/type/num/num','h4/type/realax/real'),D))) = s('h4/type/num/num',N))).
