include('Axioms/SET010^0.ax').
thf(m2_finseq_1_type, type, m2_finseq_1: $i > $i > $o).
thf(k1_numbers_type, type, k1_numbers: $i).
thf(k3_finseq_1_type, type, k3_finseq_1: $i > $i).
thf(k8_rvsum_1_type, type, k8_rvsum_1: $i > $i > $i).
thf(k6_rvsum_1_type, type, k6_rvsum_1: $i > $i).
thf(k4_rvsum_1_type, type, k4_rvsum_1: $i > $i > $i).
thf(v1_relat_1_type, type, v1_relat_1: $i > $o).
thf(v1_funct_1_type, type, v1_funct_1: $i > $o).
thf(v3_valued_0_type, type, v3_valued_0: $i > $o).
thf(v1_finseq_1_type, type, v1_finseq_1: $i > $o).
thf(m1_finseq_1_type, type, m1_finseq_1: $i > $i > $o).
thf(m1_subset_1_type, type, m1_subset_1: $i > $i > $o).
thf(k1_zfmisc_1_type, type, k1_zfmisc_1: $i > $i).
thf(k2_zfmisc_1_type, type, k2_zfmisc_1: $i > $i > $i).
thf(k5_numbers_type, type, k5_numbers: $i).
thf(t34_rvsum_1, axiom,   (! [A: $i] :  ( ( (v1_relat_1 @ A)  &  ( (v1_funct_1 @ A)  &  ( (v3_valued_0 @ A)  &  (v1_finseq_1 @ A) ) ) )  =>  (! [B: $i] :  ( ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  ( (v3_valued_0 @ B)  &  (v1_finseq_1 @ B) ) ) )  =>  ( (= @  ( (k8_rvsum_1 @ A)  @  (k6_rvsum_1 @ B) ) )  @  ( (k4_rvsum_1 @ A)  @ B) ) ) ) ) ) , file(rvsum_1, t34_rvsum_1)).
thf(redefinition_m2_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  <=>  ( (m1_finseq_1 @ B)  @ A) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(dt_m2_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ A)  =>  ( (v1_funct_1 @ B)  &  ( (v1_finseq_1 @ B)  &  ( (m1_subset_1 @ B)  @  (k1_zfmisc_1 @  ( (k2_zfmisc_1 @ k5_numbers)  @ A) ) ) ) ) ) ) ) , file(finseq_1, m2_finseq_1)).
thf(dt_m1_finseq_1, axiom,   (! [A: $i] :  (! [B: $i] :  ( ( (m1_finseq_1 @ B)  @ A)  =>  ( (v1_relat_1 @ B)  &  ( (v1_funct_1 @ B)  &  (v1_finseq_1 @ B) ) ) ) ) ) , file(finseq_1, m1_finseq_1)).
thf(cc4_seqm_3, axiom,   (! [A: $i] :  ( ( (m1_finseq_1 @ A)  @ k1_numbers)  =>  (v3_valued_0 @ A) ) ) , file(seqm_3, cc4_seqm_3)).
thf(t7_matrixr1, conjecture,   (! [A: $i] :  ( ( (m2_finseq_1 @ A)  @ k1_numbers)  =>  (! [B: $i] :  ( ( (m2_finseq_1 @ B)  @ k1_numbers)  =>  ( ( (= @  (k3_finseq_1 @ A) )  @  (k3_finseq_1 @ B) )  =>  ( (= @  ( (k8_rvsum_1 @ A)  @  (k6_rvsum_1 @ B) ) )  @  ( (k4_rvsum_1 @ A)  @ B) ) ) ) ) ) ) , file(matrixr1, t7_matrixr1)).