%   ORIGINAL: 'h4/thm/transc/DIVISION_LT_GEN_'
% 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: !D a b m n. 'h4/const/transc/division' ('h4/const/pair/,' a b) D /\ 'h4/const/prim_rec/<' m n /\ 'h4/const/arithmetic/<=' n ('h4/const/transc/dsize' D) ==> 'h4/const/realax/real_lt' (D m) (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: !D a b m n. 'h4/const/transc/division' ('h4/const/pair/,' a b) D /\ 'h4/const/prim_rec/<' m n /\ 'h4/const/arithmetic/<=' n ('h4/const/transc/dsize' D) ==> 'h4/const/realax/real_lt' (happ D m) (happ 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_3f72589,V_3f72585]: ![F, G]: (![X]: s(V_3f72585,happ(s(fun(V_3f72589,V_3f72585),F),s(V_3f72589,X))) = s(V_3f72585,happ(s(fun(V_3f72589,V_3f72585),G),s(V_3f72589,X))) => s(fun(V_3f72589,V_3f72585),F) = s(fun(V_3f72589,V_3f72585),G))).
fof('h4/thm/transc/DIVISION_LT_GEN_', conjecture, ![D, A, B, M, 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)))) & (p(s(bool,'h4/const/prim_rec/<'(s('h4/type/num/num',M),s('h4/type/num/num',N)))) & p(s(bool,'h4/const/arithmetic/<='(s('h4/type/num/num',N),s('h4/type/num/num','h4/const/transc/dsize'(s(fun('h4/type/num/num','h4/type/realax/real'),D)))))))) => 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',M))),s('h4/type/realax/real',happ(s(fun('h4/type/num/num','h4/type/realax/real'),D),s('h4/type/num/num',N)))))))).
