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IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html
At: count pairs swap 1 1 1 1 1 2
1. T : Type
2. L : T List
3. P : TT
4. n : (||L||-1)
5. (n, n+1)  ||L||||L||
6. ||swap(L;n;n+1)|| = ||L||
7. f : ||L||||L||
8. i:||L||. f(i) = (n, n+1)(i)
9. Bij(||L||; ||L||; f)
  sum(if (i<j)P(swap(L;n;n+1)[i],swap(L;n;n+1)[j]) 1
  sum(else 0 fi | i < ||L||; j < ||L||)
  =
  sum(if (f(i)<f(j))P(swap(L;n;n+1)[(f(i))],swap(L;n;n+1)[(f(j))]) 1
  sum(else 0 fi | i < ||L||; j < ||L||)
By: (Inst Thm: permute double sum
([||L||
(;||L||
(;i,j. if (i<j)P(swap(L;n;n+1)[i],swap(L;n;n+1)[j]) 1 else 0 fi
(;f
(;f])
THEN
(All ReduceSOAps)

Generated subgoals:

None

About:
listboolifthenelseintnatural_numberaddsubtractlambda
applyfunctionuniverseequalmemberimpliesall
IF YOU CAN SEE THIS go to /sfa/Nuprl/Shared/Xindentation_hack_doc.html

(29steps total) PrintForm Definitions Lemmas mb list 2 Sections MarkB generic Doc