%   ORIGINAL: h4/integer__word/w2i__lt__0
% 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
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/integer__word/w2i__i2w: !i. h4/integer/int__le (h4/integer__word/INT__MIN h4/bool/the__value) i /\ h4/integer/int__le i (h4/integer__word/INT__MAX h4/bool/the__value) ==> h4/integer__word/w2i (h4/integer__word/i2w i) = i
% Assm: h4/integer__word/ranged__int__word__nchotomy: !w. ?i. w = h4/integer__word/i2w i /\ h4/integer/int__le (h4/integer__word/INT__MIN h4/bool/the__value) i /\ h4/integer/int__le i (h4/integer__word/INT__MAX h4/bool/the__value)
% Assm: h4/integer__word/WORD__LTi: !b a. h4/words/word__lt a b <=> h4/integer/int__lt (h4/integer__word/w2i a) (h4/integer__word/w2i b)
% Assm: h4/integer__word/word__0__w2i: h4/integer__word/w2i (h4/words/n2w h4/num/0) = h4/integer/int__of__num h4/num/0
% Goal: !w. h4/integer/int__lt (h4/integer__word/w2i w) (h4/integer/int__of__num h4/num/0) <=> h4/words/word__lt w (h4/words/n2w h4/num/0)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_integeru_u_words_w2iu_u_i2w]: !i. h4/integer/int__le (h4/integer__word/INT__MIN h4/bool/the__value) i /\ h4/integer/int__le i (h4/integer__word/INT__MAX h4/bool/the__value) ==> h4/integer__word/w2i (h4/integer__word/i2w i) = i
% Assm [h4s_integeru_u_words_rangedu_u_intu_u_wordu_u_nchotomy]: !w. ?i. w = h4/integer__word/i2w i /\ h4/integer/int__le (h4/integer__word/INT__MIN h4/bool/the__value) i /\ h4/integer/int__le i (h4/integer__word/INT__MAX h4/bool/the__value)
% Assm [h4s_integeru_u_words_WORDu_u_LTi]: !b a. h4/words/word__lt a b <=> h4/integer/int__lt (h4/integer__word/w2i a) (h4/integer__word/w2i b)
% Assm [h4s_integeru_u_words_wordu_u_0u_u_w2i]: h4/integer__word/w2i (h4/words/n2w h4/num/0) = h4/integer/int__of__num h4/num/0
% Goal: !w. h4/integer/int__lt (h4/integer__word/w2i w) (h4/integer/int__of__num h4/num/0) <=> h4/words/word__lt w (h4/words/n2w h4/num/0)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q298592,TV_Q298588]: ![V_f, V_g]: (![V_x]: s(TV_Q298588,happ(s(t_fun(TV_Q298592,TV_Q298588),V_f),s(TV_Q298592,V_x))) = s(TV_Q298588,happ(s(t_fun(TV_Q298592,TV_Q298588),V_g),s(TV_Q298592,V_x))) => s(t_fun(TV_Q298592,TV_Q298588),V_f) = s(t_fun(TV_Q298592,TV_Q298588),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_integeru_u_words_w2iu_u_i2w, axiom, ![TV_u_27a]: ![V_i]: ((p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_min(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_integers_int,V_i)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))) => s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_integeru_u_words_i2w(s(t_h4s_integers_int,V_i))))) = s(t_h4s_integers_int,V_i))).
fof(ah4s_integeru_u_words_rangedu_u_intu_u_wordu_u_nchotomy, axiom, ![TV_u_27a]: ![V_w]: ?[V_i]: (s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w) = s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_integeru_u_words_i2w(s(t_h4s_integers_int,V_i))) & (p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_min(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))),s(t_h4s_integers_int,V_i)))) & p(s(t_bool,h4s_integers_intu_u_le(s(t_h4s_integers_int,V_i),s(t_h4s_integers_int,h4s_integeru_u_words_intu_u_max(s(t_h4s_bools_itself(TV_u_27a),h4s_bools_theu_u_value))))))))).
fof(ah4s_integeru_u_words_WORDu_u_LTi, axiom, ![TV_u_27a]: ![V_b, V_a]: s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a),s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b))) = s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_a))),s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_b)))))).
fof(ah4s_integeru_u_words_wordu_u_0u_u_w2i, axiom, ![TV_u_27a]: s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0)))).
fof(ch4s_integeru_u_words_w2iu_u_ltu_u_0, conjecture, ![TV_u_27a]: ![V_w]: s(t_bool,h4s_integers_intu_u_lt(s(t_h4s_integers_int,h4s_integeru_u_words_w2i(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w))),s(t_h4s_integers_int,h4s_integers_intu_u_ofu_u_num(s(t_h4s_nums_num,h4s_nums_0))))) = s(t_bool,h4s_wordss_wordu_u_lt(s(t_h4s_fcps_cart(t_bool,TV_u_27a),V_w),s(t_h4s_fcps_cart(t_bool,TV_u_27a),h4s_wordss_n2w(s(t_h4s_nums_num,h4s_nums_0)))))).
