def tupd_perfect

bend-collections-laws-crypto@1.0.0.0 · proofs/lib/array.bend:170

import Base
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

170def tupd_perfect(-T: Data, +d: Nat, +t: Tree<T>, +j: Nat, +v: T, +b: Bool, +pf: {perfect(T, d, t) == True{} : Bool}) -> {perfect(T, d, tupd(T, d, t, j, v, b)) == True{} : Bool}:
171  match d t b:
172    case 0n TLeaf{x} _:
173      {==}
174    case 0n TNode{l, r} _:
175      pf
176    case 1n+p TLeaf{x} _:
177      pf
178    case 1n+ +p TNode{+l, +r} True{}:
179      L.and_intro(perfect(T, p, tupd(T, p, l, j, v, ndec(p, j))), perfect(T, p, r), tupd_perfect(T, p, l, j, v, ndec(p, j), pf_left(T, p, l, r, pf)), pf_right(T, p, l, r, pf))
180    case 1n+ +p TNode{+l, +r} False{}:
181      L.and_intro(perfect(T, p, l), perfect(T, p, tupd(T, p, r, Nat.sub(j, SC.pow2(p)), v, ndec(p, Nat.sub(j, SC.pow2(p))))), pf_left(T, p, l, r, pf), tupd_perfect(T, p, r, Nat.sub(j, SC.pow2(p)), v, ndec(p, Nat.sub(j, SC.pow2(p))), pf_right(T, p, l, r, pf)))