%   ORIGINAL: h4/machine__ieee/fp32__sqrt__n2w
% 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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/machine__ieee/fp32__sqrt__def: !mode. h4/machine__ieee/fp32__sqrt mode = h4/combin/o h4/machine__ieee/float__to__fp32 (h4/combin/o (h4/binary__ieee/float__sqrt mode) h4/machine__ieee/fp32__to__float)
% Goal: !mode a. h4/machine__ieee/fp32__sqrt mode (h4/words/n2w a) = h4/machine__ieee/float__to__fp32 (h4/binary__ieee/float__sqrt mode (h4/machine__ieee/fp32__to__float (h4/words/n2w a)))
%   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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_machineu_u_ieees_fp32u_u_sqrtu_u_def]: !mode. h4/machine__ieee/fp32__sqrt mode = h4/combin/o h4/machine__ieee/float__to__fp32 (h4/combin/o (h4/binary__ieee/float__sqrt mode) h4/machine__ieee/fp32__to__float)
% Goal: !mode a. happ (h4/machine__ieee/fp32__sqrt mode) (h4/words/n2w a) = happ h4/machine__ieee/float__to__fp32 (happ (h4/binary__ieee/float__sqrt mode) (happ h4/machine__ieee/fp32__to__float (h4/words/n2w a)))
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_Q347289,TV_Q347285]: ![V_f, V_g]: (![V_x]: s(TV_Q347285,happ(s(t_fun(TV_Q347289,TV_Q347285),V_f),s(TV_Q347289,V_x))) = s(TV_Q347285,happ(s(t_fun(TV_Q347289,TV_Q347285),V_g),s(TV_Q347289,V_x))) => s(t_fun(TV_Q347289,TV_Q347285),V_f) = s(t_fun(TV_Q347289,TV_Q347285),V_g))).
fof(ah4s_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_machineu_u_ieees_fp32u_u_sqrtu_u_def, axiom, ![V_mode]: s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))))),h4s_machineu_u_ieees_fp32u_u_sqrt(s(t_h4s_binaryu_u_ieees_rounding,V_mode))) = s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))))),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp32),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_combins_o(s(t_fun(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_binaryu_u_ieees_floatu_u_sqrt(s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_fp32u_u_tou_u_float)))))).
fof(ch4s_machineu_u_ieees_fp32u_u_sqrtu_u_n2w, conjecture, ![V_mode, V_a]: s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))))),h4s_machineu_u_ieees_fp32u_u_sqrt(s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),h4s_wordss_n2w(s(t_h4s_nums_num,V_a))))) = s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))))),h4s_machineu_u_ieees_floatu_u_tou_u_fp32),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),happ(s(t_fun(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_binaryu_u_ieees_floatu_u_sqrt(s(t_h4s_binaryu_u_ieees_rounding,V_mode))),s(t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))),happ(s(t_fun(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),t_h4s_binaryu_u_ieees_float(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit1(t_h4s_fcps_bit0(t_h4s_ones_one)))),t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one))))),h4s_machineu_u_ieees_fp32u_u_tou_u_float),s(t_h4s_fcps_cart(t_bool,t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_fcps_bit0(t_h4s_ones_one)))))),h4s_wordss_n2w(s(t_h4s_nums_num,V_a)))))))))).
