| | Who Cites agree on common? |
|
| agree_on_common | Def agree_on_common(T;as;bs) == Case of as; nil  True ; a.as' Case of bs; nil True ; b.bs'  (a  bs) & agree_on_common(T;as';bs)  (b as) & agree_on_common(T;as;bs') a = b T & agree_on_common(T;as';bs') (recursive) |
| | | Thm*  T:Type, as,bs:T List. agree_on_common(T;as;bs) Prop |
|
| l_member | Def (x l) ==  i: . i < ||l|| & x = l[i] T |
| | | Thm* T:Type, x:T, l:T List. (x l) Prop |
|
| nat | Def == {i: | 0 i } |
| | | Thm* Type |
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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 |
|
| select | Def l[i] == hd(nth_tl(i;l)) |
| | | Thm* A:Type, l:A List, n:. 0n n < ||l|| l[n] A |
|
| length | Def ||as|| == Case of as; nil 0 ; a.as' ||as'||+1 (recursive) |
| | | Thm* A:Type, l:A List. ||l|| |
| | | Thm* ||nil|| |
|
| 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 |
|
| 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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| 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 |
