| Who Cites disjoint sublists? |
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disjoint_sublists | Def disjoint_sublists(T;L1;L2;L)
Def == f1:(||L1||||L||), f2:(||L2||||L||).
Def == increasing(f1;||L1||) & (j:||L1||. L1[j] = L[(f1(j))] T)
Def == & increasing(f2;||L2||) & (j:||L2||. L2[j] = L[(f2(j))] T)
Def == & (j1:||L1||, j2:||L2||. f1(j1) = f2(j2)) |
| | Thm* T:Type, L1,L2,L:T List. disjoint_sublists(T;L1;L2;L) 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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lelt | Def i j < k == ij & j<k |
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le | Def AB == B<A |
| | Thm* i,j:. (ij) Prop |
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not | Def A == A False |
| | Thm* A:Prop. (A) 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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select | Def l[i] == hd(nth_tl(i;l)) |
| | Thm* A:Type, l:A List, n:. 0n n<||l|| l[n] A |
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nth_tl | Def nth_tl(n;as) == if n0 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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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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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 |