ProofOps.push_room: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_ops.bend as ProofOps
Lines 146-153 of lawful-bytes@0.1.1.0/proof_ops.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_ops.bend&start_line=146&end_line=153

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

# The room test of push, as numbers.
law push_room:
  for +len: U32
  for +t: P.Tree<U32>
  for +d: Nat
  for +h: {D.ok(C.BT(len, t), d) == True{} : Bool}
  for +hc: {Nat.is_lt(D.size(C.BT(len, t)), D.cap(C.BT(len, t))) == True{} : Bool}
  {Nat.is_lt(U32.to_nat(len), Nat.mul(4n, Nat.pow(2n, d))) == True{} : Bool}

Uses (14):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  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_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.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.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/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=cap_ok_t