| Some definitions of interest. |
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int_lower | Def {...i} == {j:| ji } |
| | Thm* i:. {...i} Type |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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is_assoc_sep | Def is_assoc_sep(A; f) == is_assoc(A; x,y.(f(x,y))) |
| | Thm* f:(AAA). is_assoc_sep(A; f) Prop |
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is_commutative_sep | Def is_commutative_sep(A; f) == is_commutative(A; x,z.(f(x,z))) |
| | Thm* f:(AAA). is_commutative_sep(A; f) Prop |
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is_ident | Def is_ident(A; f; u) == x:A. f(u,x) = x & f(x,u) = x |
| | Thm* f:(AAA), u:A. is_ident(A; f; u) Prop |
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iter_via_intseg | Def Iter(f;u) i:{a..b}. e(i)
Def == if a<b f((Iter(f;u) i:{a..b-1}. e(i)),e(b-1)) else u fi
Def (recursive) |
| | Thm* f:(AAA), u:A, a,b:, e:({a..b}A). (Iter(f;u) i:{a..b}. e(i)) A |
|
le | Def AB == B<A |
| | Thm* i,j:. (ij) Prop |