Thm* eq:{T }, u:T, L:T List, v:T. v( eq) remove(eq;u;L)  v( eq) L | [remove_is_member_lemma] |
Thm* eq:{T= }, x,y:T, L:T List. x( eq) L  eq(x,y)  x( eq) remove(eq;y;L) | [not_is_member_remove_lemma] |
Thm* eq:{T= }, L:T List, x:T. x( eq) L  ( M,N:T List. L = (M @ (x.N)) & remove(eq;x;L) = (M @ N)) | [is_member_remove_lemma] |
Thm* eq:{T }, x,y:T, L:T List. x( eq) remove(eq;y;L)  x( eq) L | [remove_is_member] |