T:Type. T    (x:T, L:T List. sorted(L)  sorted(s-insert(x;L))) 

latex

Definitions

t  T, sorted(L), s-insert(x;l), P  Q, x:A. B(x), ||as||, P & Q, i  j < k, False, A, AB, {i..j}, l[i], if b t else f fi, xL. P(x), P  Q, P  Q, Prop, True, ij, b, b, , i<j, T, Unit, i=j, x. t(x), (x  l), P  Q, {T}

Lemmas

implies functionality wrt iff, member-s-insert, l member wf, l all cons, assert of bnot, not functionality wrt iff, assert of eq int, eq int wf, not wf, eqtt to assert, assert of lt int, iff transitivity, eqff to assert, squash wf, true wf, bnot of lt int, assert of le int, lt int wf, bool wf, bnot wf, assert wf, le int wf, sorted-cons, s-insert wf, sorted wf, length wf1, int seg wf, le wf, select wf, length wf2