def internal_least_trans

bend-mathlib@0.8.1.0 · sort.bend:117

import Base

117def internal_least_trans(~A: Data, ~le: A -> A -> Bool, ~le_trans: @x: A -> @y: A -> @z: A -> {le(x, y) == True{} : Bool} -> {le(y, z) == True{} : Bool} -> {le(x, z) == True{} : Bool}, +a: A, +b: A, +xs: List<&2, A>, +hab: {le(a, b) == True{} : Bool}, +hb: internal_least(~A, ~le, b, xs)) -> internal_least(~A, ~le, a, xs):
118  match xs:
119    case Nil{}:
120      {==}
121    case +h <> +t:
122      internal_least_intro(~A, ~le, a, h, t, le_trans(a, b, h, hab, internal_least_cons_le(~A, ~le, b, h, t, hb)), internal_least_trans(~A, ~le, ~le_trans, a, b, t, hab, internal_least_cons_tail(~A, ~le, b, h, t, hb)))