def wp_top

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fix64.bend:332

import Base
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-math@1.0.0.0/spec/math/generic.bend as SG
import bend-collections-laws-math@1.0.0.0/src/math/u64.bend as WU
import bend-collections-laws-math@1.0.0.0/src/math/fixed.bend as F
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/u32laws.bend as LW
import bend-collections-laws-math@1.0.0.0/proofs/lib/arith.bend as AR
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-math@1.0.0.0/proofs/math/typed/fixgen.bend as G

332def wp_top(+mp: Nat, +hp: {C.pow2(64n) == 1n+mp : Nat}, +a: WU.U64, +e: U32) -> {SG.u64_val(F.u64_wrapping_pow(a, e)) == C.low(64n, pw(a, e)) : Nat}:
333  +ih = wp_go(32n, mp, hp, e, a, WU.U64{1, 0}, U32.is_zero(e), {==}, WW.lt_of_fits(32n, vs(e), LW.vb(e)))
334  +e1 = Equal.cong(Nat, Nat, t => Nat.mod(t, 1n+mp), Nat.mul(1n, pw(a, e)), pw(a, e), AR.one_mul(pw(a, e)))
335  Equal.trans(Nat, SG.u64_val(F.u64_wrapping_pow(a, e)), Nat.mod(Nat.mul(1n, pw(a, e)), 1n+mp), C.low(64n, pw(a, e)), ih, Equal.trans(Nat, Nat.mod(Nat.mul(1n, pw(a, e)), 1n+mp), Nat.mod(pw(a, e), 1n+mp), C.low(64n, pw(a, e)), e1, Equal.sym(Nat, C.low(64n, pw(a, e)), Nat.mod(pw(a, e), 1n+mp), G.low_mod(64n, pw(a, e), mp, hp))))