is mentioned by
Thm* is_ident(A; f; u) Thm* Thm* is_assoc_sep(A; f) Thm* Thm* (a,c,b:, e:({a..b}A). Thm* (ac Thm* ( Thm* (c<b Thm* ( Thm* ((Iter(f;u) i:{a..b}. e(i)) Thm* (= Thm* (f((Iter(f;u) i:{a..c}. e(i)),f(e(c),Iter(f;u) i:{c+1..b}. e(i)))) | [iter_via_intseg_split_pluck] |
Thm* is_ident(A; f; u) Thm* Thm* is_assoc_sep(A; f) Thm* Thm* (a,b:, c:{a...b}, d:{c..b}, e:({a..b}A). Thm* ((i:{a..b}. i<c di e(i) = u) Thm* ( Thm* ((Iter(f;u) i:{a..b}. e(i)) = (Iter(f;u) i:{c..d}. e(i))) | [iter_via_intseg_amputate_units] |
Thm* is_ident(A; f; u) Thm* Thm* is_assoc_sep(A; f) Thm* Thm* (a,c,b:, e:({a..b}A). Thm* (ac Thm* ( Thm* (cb Thm* ( Thm* ((Iter(f;u) i:{a..b}. e(i)) Thm* (= Thm* (f((Iter(f;u) i:{a..c}. e(i)),Iter(f;u) i:{c..b}. e(i))) | [iter_via_intseg_split_mid] |
Thm* is_commutative_sep(A; f) Thm* Thm* is_ident(A; f; u) Thm* Thm* is_assoc_sep(A; f) Thm* Thm* (a,b:, e,g:({a..b}A). Thm* (f((Iter(f;u) i:{a..b}. e(i)),Iter(f;u) i:{a..b}. g(i)) Thm* (= Thm* ((Iter(f;u) i:{a..b}. f(e(i),g(i))) Thm* ( A) | [iter_via_intseg_comp_binop] |
[is_assoc_intadd] | |
[is_assoc_intmul] |
Try larger context:
DiscrMathExt
IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html