Rank | Theorem | Name |
3 | Thm* L:T List, P:( ||L|| Prop).
Thm* ( x: ||L||. Dec(P(x)))
Thm* 
Thm* ( L1,L2:T List, f1:( ||L1||  ||L||), f2:( ||L2||  ||L||).
Thm* (interleaving_occurence(T;L1;L2;L;f1;f2)
Thm* (& ( i: ||L1||. P(f1(i))) & ( i: ||L2||. P(f2(i)))
Thm* (& ( i: ||L||.
Thm* (& ((P(i)  ( j: ||L1||. f1(j) = i))
Thm* (& (& ( P(i)  ( j: ||L2||. f2(j) = i)))) | [interleaving_split] |
cites the following: |
0 | Thm* m: , P:( m Prop).
Thm* ( i: m. Dec(P(i)))
Thm* 
Thm* ( n,k: , f:( n  m), g:( k  m).
Thm* (increasing(f;n)
Thm* (& increasing(g;k)
Thm* (& ( i: n. P(f(i)))
Thm* (& ( j: k. P(g(j)))
Thm* (& ( i: m. ( j: n. i = f(j)) ( j: k. i = g(j)))) | [increasing_split] |
1 | Thm* L:T List, n: , f:( n  ||L||).
Thm* increasing(f;n)
Thm* 
Thm* ( L1:T List. ||L1|| = n & sublist_occurence(T;L1;L;f)) | [range_sublist] |
2 | Thm* m,n,k: , f:( n  m), g:( k  m).
Thm* increasing(f;n)
Thm* 
Thm* increasing(g;k)
Thm* 
Thm* ( i: m. ( j: n. i = f(j)) ( j: k. i = g(j)))
Thm* 
Thm* ( j1: n, j2: k. f(j1) = g(j2))  m = n+k  | [disjoint_increasing_onto] |