def and_low_hx

bend-collections-laws-math@1.0.0.0 · proofs/lib/u32.bend:221

import Base
import bend-collections-laws-math@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-math@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-math@1.0.0.0/proofs/lib/lemmas/spec/numeric.bend as S

221def and_low_hx(+m: Nat, +d: Nat, +xb: Bool, +xt: Word(m), +hx: {Nat.is_lt(Nat.add(S.bit_value(xb), Nat.double(S.unsigned(m, xt))), SC.pow2(d)) == True{} : Bool}) -> {Nat.is_lt(S.unsigned(m, xt), SC.pow2(and_low_prev(d))) == True{} : Bool}:
222  match d:
223    case 0n:
224      %Equal.sym(Nat, S.unsigned(m, xt), 0n, N.bit_split_val(xb, False{}, S.unsigned(m, xt), 0n, lt_one_zero(Nat.add(S.bit_value(xb), Nat.double(S.unsigned(m, xt))), hx))) : {Nat.is_lt(_, 1n) == True{} : Bool}
225      {==}
226    case 1n+k:
227      N.bit_double_lt(xb, S.unsigned(m, xt), SC.pow2(k), hx)