| Who Cites interleaving? |
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interleaving | Def interleaving(T;L1;L2;L) == ||L|| = ||L1||+||L2|| & disjoint_sublists(T;L1;L2;L) |
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disjoint_sublists | Def disjoint_sublists(T;L1;L2;L) == f1:( ||L1||![](FONT/dash.png) ![](FONT/then_med.png) ||L||), f2:( ||L2||![](FONT/dash.png) ![](FONT/then_med.png) ||L||). increasing(f1;||L1||) & ( j: ||L1||. L1[j] = L[(f1(j))] T) & increasing(f2;||L2||) & ( j: ||L2||. L2[j] = L[(f2(j))] T) & ( j1: ||L1||, j2: ||L2||. f1(j1) = f2(j2)) |
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length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | Thm* A:Type, l:A List. ||l|| ![](FONT/int.png) |
| | Thm* ||nil|| ![](FONT/int.png) |
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nat | Def == {i: | 0 i } |
| | Thm* Type |
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increasing | Def increasing(f;k) == i: (k-1). f(i) < f(i+1) |
| | Thm* k: , f:( k![](FONT/dash.png) ![](FONT/then_med.png) ). 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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lelt | Def i j < k == i j & j < k |
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le | Def A B == B < A |
| | Thm* i,j: . (i j) Prop |
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not | Def A == A ![](FONT/eq.png) False |
| | Thm* A:Prop. ( A) Prop |
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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n: . 0 n ![](FONT/eq.png) n < ||l|| ![](FONT/eq.png) l[n] A |
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nth_tl | Def nth_tl(n;as) == if n![](FONT/le.png) 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 ![](FONT/eq.png) hd(l) A |
| | Thm* A:Type, l:A List . hd(l) A |
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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![](FONT/le.png) j == ![](FONT/not.png) j < i |
| | Thm* i,j: . (i![](FONT/le.png) j) ![](FONT/bool.png) |
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lt_int | Def i < j == if i < j true ; false fi |
| | Thm* i,j: . (i < j) ![](FONT/bool.png) |
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bnot | Def ![](FONT/not.png) b == if b false else true fi |
| | Thm* b: . ![](FONT/not.png) b ![](FONT/bool.png) |