| Some definitions of interest. |
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iff | Def P Q == (P Q) & (P Q) |
| | Thm* A,B:Prop. (A B) Prop |
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sublist | Def L1 L2
Def == f:(||L1||||L2||).
Def == increasing(f;||L1||) & (j:||L1||. L1[j] = L2[(f(j))] T) |
| | Thm* T:Type, L1,L2:T List. L1 L2 Prop |
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increasing | Def increasing(f;k) == i:(k-1). f(i)<f(i+1) |
| | Thm* k:, f:(k). increasing(f;k) Prop |
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int_seg | Def {i..j} == {k:| i k < j } |
| | Thm* m,n:. {m..n} Type |
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iseg | Def l1 l2 == l:T List. l2 = (l1 @ l) |
| | Thm* T:Type, l1,l2:T List. l1 l2 Prop |
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nat | Def == {i:| 0i } |
| | Thm* Type |
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le | Def AB == B<A |
| | Thm* i,j:. (ij) Prop |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| |
| | Thm* ||nil|| |
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rev_implies | Def P Q == Q P |
| | Thm* A,B:Prop. (A B) Prop |
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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n:. 0n n<||l|| l[n] A |