ProofShift.shift_ok_t: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_shift.bend as ProofShift
Lines 498-505 of lawful-bytes@0.1.1.0/proof_shift.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&start_line=498&end_line=505

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
import lawful-bytes@0.1.1.0/bytes.bend as B
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/proof_tree.bend as P

law shift_ok_t:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +k: U32
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +hk: {Nat.is_le(U32.to_nat(k), D.size(C.BT(len, t))) == True{} : Bool}
  {D.ok(B.shift(C.BT(len, t), k), d) == True{} : Bool}

Uses (27):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.sym
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  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.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.is_le
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.sub
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_base.bend&name=subst
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=Tree
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=at
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=shift
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=shift.go
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/bytes.bend&name=truncate
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=Bytes
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/defs.bend&name=size
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=BT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_ops.bend&name=truncate_ok_t
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=SGT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=sgt_ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=shift_go_eq
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_shift.bend&name=sub_le
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=is_le_to_nat
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_u32.bend&name=to_nat_sub_le