| Who Cites sublist? |
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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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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n: . 0 n  n<||l||  l[n] A |
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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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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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nth_tl | Def nth_tl(n;as) == if n 0 as else nth_tl(n-1;tl(as)) fi (recursive) |
| | Thm* A:Type, as:A List, i: . nth_tl(i;as) A List |
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hd | Def hd(l) == Case of l; nil "?" ; h.t h |
| | Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
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lelt | Def i j < k == i j & j<k |
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tl | Def tl(l) == Case of l; nil nil ; h.t t |
| | Thm* A:Type, l:A List. tl(l) A List |
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le_int | Def i j ==  j< i |
| | Thm* i,j: . (i j)  |
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le | Def A B == B<A |
| | Thm* i,j: . (i j) Prop |
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lt_int | Def i< j == if i<j true ; false fi |
| | Thm* i,j: . (i< j)  |
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bnot | Def  b == if b false else true fi |
| | Thm* b: .  b  |
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not | Def A == A  False |
| | Thm* A:Prop. ( A) Prop |