def pow32
bend-collections-laws-math@1.0.0.0 · proofs/math/u64/u64div.bend:80
import bend-collections-laws-math@1.0.0.0/proofs/math/u64/u64div.bend as U64div
import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/logic.bend as L
import bend-collections-laws-math@1.0.0.0/proofs/lib/word.bend as WD
import bend-collections-laws-math@1.0.0.0/proofs/lib/u32div.bend as UD
80def pow32(+k: Nat, +hk: {Nat.is_lt(k, 32n) == True{} : Bool}, +one: Nat, +h1: {one == 1n : Nat}, +c: U32, +hc: {c == U32{WD.pw(32n, k)} : U32}) -> {UD.v(c) == WD.sc(k, one) : Nat}:
81 +e = Equal.trans(Nat, UD.v(U32{WD.pw(32n, k)}), WD.uw(32n, WD.pw(32n, k)), WD.sc(k, one), UD.vw(WD.pw(32n, k)), WD.pwv(32n, k, hk, one, h1, WD.pw(32n, k), {==}))
82 L.subst(U32, z => {UD.v(z) == WD.sc(k, one) : Nat}, U32{WD.pw(32n, k)}, c, Equal.sym(U32, c, U32{WD.pw(32n, k)}, hc), e)