Thm* a,b: , P:({a..b } Prop). ( i:{a..b }. P(i))  (Or i:{a..b }. P(i)) | [exist_intseg_vs_iter_or] |
Thm* a,b: , P:({a..b } Prop). b a  ( i:{a..b }. P(i)) | [exist_intseg_null] |
Thm* a,b: , P:({a..b } Prop).
Thm* a<b  (( i:{a..b }. P(i))  ( i:{a..(b-1) }. P(i)) P(b-1)) | [or_via_exist_intseg_split_last] |
Thm* a,b: , P:({a..b } Prop).
Thm* a<b
Thm* 
Thm* ( c: . b = c+1  (( i:{a..b }. P(i))  ( i:{a..c }. P(i)) P(c))) | [or_via_exist_intseg_notnull] |
Thm* a,b: , P:({a..b } Prop). ( i:{a..b }. P(i))  (And i:{a..b }. P(i)) | [all_intseg_vs_iter_and] |
Thm* a,b: , P:({a..b } Prop).
Thm* a<b  (( i:{a..b }. P(i))  ( i:{a..(b-1) }. P(i)) & P(b-1)) | [and_via_all_intseg_split_last] |
Thm* a,b: , P:({a..b } Prop).
Thm* a<b
Thm* 
Thm* ( c: . b = c+1  (( i:{a..b }. P(i))  ( i:{a..c }. P(i)) & P(c))) | [and_via_all_intseg_notnull] |
Thm* P:(     Prop).
Thm* ( a: , b:{...a}. P(a,b))
Thm* 
Thm* ( a: , b:{a+1...}. ( c:{a..b }. P(a,c))  P(a,b))  ( a,b: . P(a,b)) | [all_int_segs_by_upper_ind] |
Thm* P:(     Prop), a: .
Thm* ( b:{...a}. P(a,b))
Thm* 
Thm* ( b:{a+1...}. ( c:{a..b }. P(a,c))  P(a,b))  ( b: . P(a,b)) | [int_segs_from_base_by_upper_ind] |
Thm* P:(     Prop), a: .
Thm* ( b:{...a}. P(a,a)  P(a,b))  ( b:{a...}. P(a,b))  ( b: . P(a,b)) | [split_int_domain_by_norm_lower] |
Thm* P:(     Prop), a: .
Thm* ( b:{a...}. ( c:{a..b }. P(a,c))  P(a,b))  ( b:{a...}. P(a,b)) | [int_seg_upper_ind] |
Thm* P:(     Prop).
Thm* ( a: , b:{...a}. P(a,b))
Thm* 
Thm* ( a: . ( b:{...a}. P(a,b))  ( b:{a...}. P(a,b)))  ( a,b: . P(a,b)) | [all_int_pairs_via_all_splits] |
Thm* P:(     Prop), a: .
Thm* ( b:{...a}. P(a,b))
Thm* 
Thm* (( b:{...a}. P(a,b))  ( b:{a...}. P(a,b)))  ( b: . P(a,b)) | [split_int_domain] |
Thm* f:(A A A). is_commutative_sep(A; f) Prop | [is_commutative_sep_wf] |
Thm* f:(A A A). is_commutative(A; x,z.f(x,z)) Prop | [is_commutative_wf] |
Thm* f:(A A A). is_assoc_sep(A; f) Prop | [is_assoc_sep_wf] |
Thm* f:(A A A), u:A. is_ident(A; f; u) Prop | [is_ident_wf] |