ProofGrow.ginv: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_grow.bend as ProofGrow
Lines 379-394 of lawful-bytes@0.1.1.0/proof_grow.bend: https://jend.leeeet.dev/read.txt?path=lawful-bytes@0.1.1.0/proof_grow.bend&start_line=379&end_line=394

import Base
import lawful-bytes@0.1.1.0/proof_core.bend as C
import lawful-arrays@0.1.0.0/defs.bend as A
import lawful-arrays@0.1.0.0/proof_tree.bend as P
import lawful-arrays@0.1.0.0/proof_index.bend as I

# Writing word i keeps the copied prefix and extends it by one word.
law ginv:
  for +t: P.Tree<U32>
  for +td: P.Tree<U32>
  for +i: U32
  for +d: Nat
  for +e: Nat
  for +hft: {A.full(U32, P.fromT(U32, t), d) == True{} : Bool}
  for +hfd: {A.full(U32, P.fromT(U32, td), e) == True{} : Bool}
  for +hd: {Nat.is_le(d, 29n) == True{} : Bool}
  for +he29: {Nat.is_le(e, 29n) == True{} : Bool}
  for +hjd: {Nat.is_lt(U32.to_nat(i), Nat.pow(2n, d)) == True{} : Bool}
  for +hje: {Nat.is_lt(U32.to_nat(i), Nat.pow(2n, e)) == True{} : Bool}
  for +ei1: {U32.to_nat((i + 1 : U32)) == Nat.add(U32.to_nat(i), 1n) : Nat}
  for +hinv: {List.take(&2, U32, C.WL(td), U32.to_nat(i)) == List.take(&2, U32, C.WL(t), U32.to_nat(i)) : List<&2, U32>}
  {List.take(&2, U32, C.WL(I.set_tree(U32, td, i, C.WD(t, i))), U32.to_nat((i + 1 : U32))) == List.take(&2, U32, C.WL(t), U32.to_nat((i + 1 : U32))) : List<&2, U32>}

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=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.append
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.length
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.set
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List.take
  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.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/defs.bend&name=full
  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_index.bend&name=set_tree
  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-arrays@0.1.0.0/proof_tree.bend&name=fromT
  https://jend.leeeet.dev/definition.txt?path=lawful-arrays@0.1.0.0/proof_tree.bend&name=view_length
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=WD
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=WL
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=wd_get
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_core.bend&name=wl_set
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_grow.bend&name=take_succ_get
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_seq.bend&name=take_set_succ