| | Who Cites l before? |
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| l_before | Def x before y  l == sublist(T;[x; y];l) |
| | | Thm*  T:Type, l:T List, x,y:T. x before y l Prop |
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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)) |
| | | 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 |
| | | Thm* A:Type, l:A List . hd(l) A |
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| lelt | Def i j < k == ij & 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 ij ==  j < i |
| | | Thm* i,j:. (ij)  |
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| le | Def AB == B < A |
| | | Thm* i,j:. (ij) 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 |
