ProofGrow.gtake: law of lawful-bytes@0.1.1.0
Import: import lawful-bytes@0.1.1.0/proof_grow.bend as ProofGrow
Lines 414-429 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=414&end_line=429

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

# The loop copies words i .. i+n-1 of t.
law gtake:
  for +n: Nat
  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 +he: {Nat.is_le(d, e) == True{} : Bool}
  for +he29: {Nat.is_le(e, 29n) == True{} : Bool}
  for +hn: {Nat.is_le(Nat.add(U32.to_nat(i), n), Nat.pow(2n, d)) == True{} : Bool}
  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(gtree(n, t, td, i)), Nat.add(U32.to_nat(i), n)) == List.take(&2, U32, C.WL(t), Nat.add(U32.to_nat(i), n)) : List<&2, U32>}

Uses (31):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Equal.cong
  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=List
  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.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/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-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=full_set
  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_grow.bend&name=ginv
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_grow.bend&name=gtree
  https://jend.leeeet.dev/definition.txt?path=lawful-bytes@0.1.1.0/proof_grow.bend&name=ol_room
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=add_zero
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=le_add_r
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=lt_le_trans
  https://jend.leeeet.dev/definition.txt?path=lawful-words@0.1.0.0/proof_nat.bend&name=pow_le