law gso

lawful-arrays@0.1.0.0 · proof_index.bend:183

import Base
import lawful-arrays@0.1.0.0/defs.bend as D
import lawful-arrays@0.1.0.0/proof_tree.bend as P

183# What a swap hands back is the leaf it replaced.
184law gso:
185  for -T: Data
186  for +d: Nat
187  for +t: P.Tree<T>
188  for +n: U32
189  for +i: U32
190  for +v: T
191  for +z: Bool
192  for +hf: {D.full(T, P.fromT(T, t), d) == True{} : Bool}
193  for +hn: {U32.to_nat(n) == Nat.pow(2n, d) : Nat}
194  for +hi: {Nat.is_lt(U32.to_nat(i), Nat.pow(2n, d)) == True{} : Bool}
195  for +hz: {U32.is_lt(i, U32.shr(n)) == z : Bool}
196  {Some{Pair.snd(Array<T>, T, Array.swap.go(T, P.fromT(T, t), n, i, v, z))}
197    == List.get(&2, T, D.view(T, P.fromT(T, t)), U32.to_nat(i)) : Maybe<&2, T>}