Rank | Theorem | Name |
3 | Thm* n: , R:( n  n Prop), x,y: n. (x (R^*) y)  ( k: (n+1). x R^k y) | [rel_star_finite] |
cites the following: |
1 | Thm* P:(  Prop). ( i: . ( j: . j<i  P(j))  P(i))  ( i: . P(i)) | [comp_nat_ind_a] |
1 | Thm* k,m: . ( f:( k  m). Inj( k; m; f))  k m | [injection_le] |
2 | Thm* R:(T T Prop), k: , x,y:T.
Thm* (x R^k y)
Thm* 
Thm* ( L:T List.
Thm* (||L|| = k+1 & L[0] = x & last(L) = y & ( i: k. L[i] R L[(i+1)])) | [rel_exp_list] |
0 | Thm* as,bs:T List. ||as @ bs|| = ||as||+||bs||  | [length_append] |
1 | Thm* as,bs:T List, i: ||as||. (as @ bs)[i] = as[i] | [select_append_front] |
1 | Thm* as,bs:T List, i:{||as||..(||as||+||bs||) }. (as @ bs)[i] = bs[(i-||as||)] | [select_append_back] |
0 | Thm* as:A List, n:{0...||as||}. ||nth_tl(n;as)|| = ||as||-n  | [length_nth_tl] |
0 | Thm* as:A List, n:{0...||as||}. ||firstn(n;as)|| = n  | [length_firstn] |
1 | Thm* as:T List, n:{0...||as||}, i: (||as||-n). nth_tl(n;as)[i] = as[(i+n)] | [select_nth_tl] |
1 | Thm* as:T List, n:{0...||as||}, i: n. firstn(n;as)[i] = as[i] | [select_firstn] |