| | Who Cites sublist? |
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| sublist | Def sublist(T;L1;L2)
== f:( ||L1||  ||L2||). increasing(f;||L1||) & ( j: ||L1||. L1[j] = L2[(f(j))] T) |
| | | Thm* T:Type, L1,L2:T List. sublist(T;L1;L2) Prop |
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| select |
Def l[i] == hd(nth_tl(i;l)) |
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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) |
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Thm* A:Type, l:A List. ||l||  |
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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) |
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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 |
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Thm* A:Type, l:A List. ||l|| 1  hd(l) A |
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Thm* A:Type, l:A List . 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 |
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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 |