def internal_insert_step

bend-mathlib@0.8.1.0 · sort.bend:69

import Base
import bend-mathlib@0.8.1.0/list.bend as MList
import bend-mathlib@0.8.1.0/perm.bend as MPerm

69def internal_insert_step(~A: Data, ~le: A -> A -> Bool, ~le_total: @x: A -> @y: A -> {le(x, y) == False{} : Bool} -> {le(y, x) == True{} : Bool}, b: Bool, +x: A, +y: A, +t: List<&2, A>, e: {le(x, y) == b : Bool}, +h: MList.sorted_by(~A, ~le, y <> t)) -> MList.sorted_by(~A, ~le, Bool.pick(List<&2, A>, b, x <> y <> t, y <> MPerm.insert_by(~A, ~le, x, t))):
70  match b:
71    case True{}:
72      internal_sorted_cons_cons_intro(~A, ~le, x, y, t, e, h)
73    case False{}:
74      internal_sorted_cons_ins(~A, ~le, ~le_total, t, y, x, le_total(x, y, e), h)