def AP.swap_eq

bend-osdev-array@0.1.0.1 · PROOF.bend:607

import Base

607def AP.swap_eq(-T: Data, t: AP.Tree<T>, n: U32, +i: U32, v: T, z: Bool) -> {Array.swap.go(T, AP.build(T, t), n, i, v, z) == (AP.build(T, AP.swap_t(T, t, n, i, v, z)), AP.swap_v(T, t, n, i, v, z)) : Array<T> & T}:
608  match t z:
609    case APLeaf{x} _:
610      {==}
611    case APNode{xs, ys} True{}:
612      +h = U32.shr(n)
613      +z1 = U32.is_lt(i, U32.shr(h))
614      %Equal.sym(Array<T> & T, Array.swap.go(T, AP.build(T, xs), h, i, v, z1), (AP.build(T, AP.swap_t(T, xs, h, i, v, z1)), AP.swap_v(T, xs, h, i, v, z1)), AP.swap_eq(T, xs, h, i, v, z1)) : {Array.swap.lo(T, AP.build(T, ys), _) == (ANode{AP.build(T, AP.swap_t(T, xs, h, i, v, z1)), AP.build(T, ys)}, AP.swap_v(T, xs, h, i, v, z1)) : Array<T> & T}
615      {==}
616    case APNode{xs, ys} False{}:
617      +h = U32.shr(n)
618      +j = U32.sub(i, h)
619      +z1 = U32.is_lt(j, U32.shr(h))
620      %Equal.sym(Array<T> & T, Array.swap.go(T, AP.build(T, ys), h, j, v, z1), (AP.build(T, AP.swap_t(T, ys, h, j, v, z1)), AP.swap_v(T, ys, h, j, v, z1)), AP.swap_eq(T, ys, h, j, v, z1)) : {Array.swap.hi(T, AP.build(T, xs), _) == (ANode{AP.build(T, xs), AP.build(T, AP.swap_t(T, ys, h, j, v, z1))}, AP.swap_v(T, ys, h, j, v, z1)) : Array<T> & T}
621      {==}