def AP.from_nat

bend-osdev-array@0.1.0.1 · PROOF.bend:987

import Base
import bend-osdev-array@0.1.0.1/array.bend as A

987# from_nat then to_nat is the identity below 2^d, d <= 32
988def AP.from_nat(k: Nat, +d: Nat, +h: {Nat.is_lt(k, A.Arrays.slots(d)) == True{} : Bool}, +hd: {Nat.is_le(d, 32n) == True{} : Bool}) -> {U32.to_nat(U32.from_nat(k)) == k : Nat}:
989  match k:
990    case 0n:
991      {==}
992    case 1n+ +p:
993      +ih = AP.from_nat(p, d, AP.lt_succ_l(p, A.Arrays.slots(d), h), hd)
994      Equal.trans(Nat, U32.to_nat(U32.inc(U32.from_nat(p))), 1n+U32.to_nat(U32.from_nat(p)), 1n+p, AP.u32_inc(U32.from_nat(p), d, AP.lt_rw(U32.to_nat(U32.from_nat(p)), p, A.Arrays.slots(d), ih, h), hd), AP.succ_cong(U32.to_nat(U32.from_nat(p)), p, ih))