Tree.partial_zero: 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 232-237 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=232&end_line=237

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/proofs/lib/nat.bend as N
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

def partial_zero(+fs: List<&2,T.Out>, +o: T.Out, +t: K.Stack, +hl: {Nat.is_lt(SC.length(T.Out,fs),1n) == True{} : Bool}) -> {K.finish(push_all(E(0n,t),cvs(fs)),o) == K.finish(t,S.tree(0n,SC.append(T.Out,fs,Con{o,Nil{}}))) : T.Out}:
  match fs:
    case Nil{}:
      %Equal.sym(K.Stack,E(0n,t),t,E_zero(t)) : {K.finish(_,o) == K.finish(t,S.tree(0n,Con{o,Nil{}})) : T.Out}
      {==}
    case Con{+f,+r}: Empty.absurd({K.finish(push_all(E(0n,t),cvs(Con{f,r})),o) == K.finish(t,S.tree(0n,SC.append(T.Out,Con{f,r},Con{o,Nil{}}))) : T.Out},N.lt_zero_absurd(SC.length(T.Out,r),hl))

Uses (16):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Bool
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Empty.absurd
  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=Nat.is_lt
  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=E_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=push_all
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=lt_zero_absurd
  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=append
  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/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=finish
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake3/types.bend&name=Out