def hstep

bend-collections-laws-math@1.0.0.0 · proofs/math/typed/fixbytes.bend:323

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/spec/math/fixed.bend as SF
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

323# one Horner step on both sides, carrying the bound
324def hstep(+k: Nat, +hk: {Nat.is_le(Nat.add(8n, k), 64n) == True{} : Bool}, r: Maybe<&2, WU.U64>, +S: Maybe<&2, Nat>, +es: {SF.mval(~WU.U64, ~SG.u64_val, r) == S : Maybe<&2, Nat>}, +hr: {bnd(k, SF.mval(~WU.U64, ~SG.u64_val, r)) == True{} : Bool}, +b: U32) -> {SF.mval(~WU.U64, ~SG.u64_val, F.dig64(r, F.is_byte(b), b)) == SF.digit_on(S, C.fits(8n, v(b)), v(b)) : Maybe<&2, Nat>}:
325  Equal.trans(Maybe<&2, Nat>, SF.mval(~WU.U64, ~SG.u64_val, F.dig64(r, F.is_byte(b), b)), SF.digit_on(SF.mval(~WU.U64, ~SG.u64_val, r), C.fits(8n, v(b)), v(b)), SF.digit_on(S, C.fits(8n, v(b)), v(b)), d64_val(k, hk, r, hr, b), Equal.cong(Maybe<&2, Nat>, Maybe<&2, Nat>, t => SF.digit_on(t, C.fits(8n, v(b)), v(b)), SF.mval(~WU.U64, ~SG.u64_val, r), S, es))