ProofBytes.byte_shln_low.k: def of lawful-words@0.1.0.0
Import: import lawful-words@0.1.0.0/proof_bytes.bend as ProofBytes
Lines 691-704 of lawful-words@0.1.0.0/proof_bytes.bend: https://jend.leeeet.dev/read.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&start_line=691&end_line=704

import Base
import lawful-words@0.1.0.0/defs.bend as D
import lawful-words@0.1.0.0/proof_nat.bend as N

def byte_shln_low.k(+w: U32, +s: Nat, +j: Nat, +hj: {Nat.is_lt(j, s) == True{} : Bool}, +k: Nat) ->
  {D.bit(D.byte(U32.shln(w, Nat.mul(8n, s)), j), k) == D.bit(0, k) : Bool}:
  +l = Nat.is_lt(k, 8n)
  +i = Nat.add(Nat.mul(8n, j), k)
  +s8 = Nat.mul(8n, s)
  %Equal.sym(Bool, D.bit(D.byte(U32.shln(w, s8), j), k), Bool.and(l, D.bit(U32.shln(w, s8), i)), bit_byte(U32.shln(w, s8), j, k)) :
    {_ == D.bit(0, k) : Bool}
  %Equal.sym(Bool, D.bit(U32.shln(w, s8), i), Bool.and(Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8)))), bit_shln(w, s8, i)) :
    {Bool.and(l, _) == D.bit(0, k) : Bool}
  %Equal.sym(Bool, D.bit(0, k), False{}, bit_zero(k)) :
    {Bool.and(l, Bool.and(Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8))))) == _ : Bool}
  blow(l, Nat.is_le(s8, i), Bool.and(Nat.is_lt(i, 32n), D.bit(w, Nat.sub(i, s8))),
    hk => lt_not_le(i, s8, N.lt_le_trans(i, Nat.mul(8n, 1n+j), s8, lt_mul8(j, k, hk),
      N.le_mul_l(8n, 1n+j, s, %Equal.sym(Bool, Nat.is_le(1n+j, s), Nat.is_lt(j, s), N.le_succ_lt(j, s)) : {_ == True{} : Bool}; hj))))

Uses (22):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool.and
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.is_lt
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.shln
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=bit
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/defs.bend&name=byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_byte
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_shln
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=bit_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=blow
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=lt_mul8
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_bytes.bend&name=lt_not_le
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_mul_l
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_succ_lt
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans