Thm* P:(T  ), T':Type, f:({x:T| P(x) } T'), L:T List, x,y:{x:T| P(x) }. x before y L  f(x) before f(y) mapfilter(f;P;L) | [mapfilter_before] |
Thm* f:(T T'), x,y:T, s:T List. x before y s  f(x) before f(y) map(f;s) | [map_before] |
Thm* L:T List, x,y:T. x before y L  ( L1,L2,L3:T List. L = (L1 @ [x] @ L2 @ [y] @ L3)) | [l_before-iff] |
Thm* L:T List, x,y:T. x before y L  ( A,B:T List. L = (A @ B) & (x A) & (y B)) | [l_before_decomp] |
Thm* A,B:T List, x,y:T. x before y A @ B  x before y A x before y B (x A) & (y B) | [l_before_append_iff] |