ProofAppend.step_cap: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_append.bend as ProofAppend
Lines 187-195 of lawful-bytes@0.1.1.0/proof_append.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&start_line=187&end_line=195

import Base
import lawful-bytes@0.1.1.0/defs.bend as D
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 step_cap:
  for +ld: U32
  for +td: P.Tree<U32>
  for +d: Nat
  for +x: U32
  for +k: Nat
  for +hd: {D.ok(C.BT(ld, td), d) == True{} : Bool}
  for +hc: {Nat.is_le(Nat.add(U32.to_nat(ld), 1n+k), D.cap(C.BT(ld, td))) == True{} : Bool}
  {Nat.is_le(Nat.add(U32.to_nat((ld + 1 : U32)), k), D.cap(C.BT((ld + 1 : U32), PT(ld, td, x)))) == True{} : Bool}

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=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.mul
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.pow
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32.add
  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/defs.bend&name=cap
  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/proof_append.bend&name=PT
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=le_shift
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=step_ok
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_append.bend&name=step_room
  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_core.bend&name=inc_fits
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=ok_d
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_ops.bend&name=cap_ok_t