Thm* f:(  (T List)), t,t': .
Thm* t<t'  concat(map(f;upto(t))) @ (f(t)) concat(map(f;upto(t'))) | [concat_map_upto] |
Thm* f:(Top Top), n: , l:Top List. firstn(n;map(f;l)) ~ map(f;firstn(n;l)) | [firstn_map] |
Thm* t',m: , T:Type, f:(  T), P:(T  ).
Thm* m+1 ||filter(P;map(f;upto(t')))||
Thm* 
Thm* ( t: . P(f(t)) & ||filter(P;map(f;upto(t)))|| = m ) | [filter_map_upto2] |
Thm* i,j: .
Thm* i<j
Thm* 
Thm* ( f:(  T), P:(T  ).
Thm* (P(f(i))  ||filter(P;map(f;upto(i)))||<||filter(P;map(f;upto(j)))||) | [filter_map_upto] |
Thm* f:(T T'), L:T List, x',y':T'.
Thm* x' before y' map(f;L)  ( x,y:T. x before y L & f(x) = x' & f(y) = y') | [before-map] |
Thm* m: , n: (m+1). upto(m) ~ (upto(n) @ map( x.x+n;upto(m-n))) | [upto_decomp] |
Thm* f:Top, T:Type, L:T List, i: ||L||. map(f;L)[i] ~ (f(L[i])) | [select-map] |
Thm* f:Top, T:Type, L:T List. ||map(f;L)|| ~ ||L|| | [length-map] |
Thm* L:Top List. map( x.x;L) ~ L | [map-id] |
Thm* f:(A B), l:A List. map(f;l) = nil  l = nil | [map_is_nil] |
Thm* as:Top List, f,g:Top. map(g;map(f;as)) ~ map(g o f;as) | [map-map] |