Tree.complete: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend as Tree
Lines 220-228 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&start_line=220&end_line=228

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/types.bend as T
import bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/blake3.bend as K
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/blake/blake3.bend as S

# A stack with g empty low slots absorbs the chaining values of 2^g outputs
# as one complete subtree pushed at slot g.
def complete(+g: Nat, +xs: List<&2,T.Out>, +t: K.Stack, +hl: {SC.length(T.Out,xs) == SC.pow2(g) : Nat}) -> {push_all(E(g,t),cvs(xs)) == E(g,K.push(t,S.cv(S.tree(g,xs)))) : K.Stack}:
  match g:
    case 0n: complete_zero(xs,t,hl)
    case 1n+p:
      complete_step(p,xs,t,pow_ne(xs,1n+p,hl),half_not_nil(xs,p,hl),
        complete(p,SC.take(T.Out,xs,SC.pow2(p)),lift(t),half_len_take(xs,p,hl)),
        complete(p,SC.drop(T.Out,xs,SC.pow2(p)),K.SFull{S.cv(S.tree(p,SC.take(T.Out,xs,SC.pow2(p)))),t},half_len_drop(xs,p,hl)))

Uses (21):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=E
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=complete_step
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=complete_zero
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=cvs
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=half_len_drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=half_len_take
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=half_not_nil
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=lift
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=pow_ne
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/tree.bend&name=push_all
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/blake/blake3.bend&name=cv
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/blake/blake3.bend&name=tree
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=drop
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=length
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=pow2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=take
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/blake3.bend&name=Stack
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/blake3.bend&name=push
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/types.bend&name=Out