Loop.len_init2: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/loop.bend as Loop
Lines 48-51 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/loop.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/blake/blake3/loop.bend&start_line=48&end_line=51

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/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as SC

def len_init2(+r: List<&2,T.Out>, +x: T.Out) -> {SC.length(T.Out,init2(r,x)) == SC.length(T.Out,r) : Nat}:
  match r:
    case Nil{}: {==}
    case Con{+y,+q}: N.succ_cong(SC.length(T.Out,init2(q,y)),SC.length(T.Out,q),len_init2(q,y))

Uses (6):
  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/loop.bend&name=init2
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=succ_cong
  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/types.bend&name=Out