Top.cat2_eq: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/top.bend as Top
Lines 81-86 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/top.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/top.bend&start_line=81&end_line=86

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend as SE
import bend-collections-laws-crypto@1.0.0.0/src/crypto/ed25519/ed25519.bend as E
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend as BY

def cat2_eq(+x: List<&2, U32>, +sx: List<&2, U32>, +y: List<&2, U32>, +sy: List<&2, U32>, +m: List<&2, U32>, +ex: {x == sx : List<&2, U32>}, +ey: {y == sy : List<&2, U32>}) -> {E.cat(x, E.cat(y, m)) == SE.cat(sx, SE.cat(sy, m)) : List<&2, U32>}:
  +e1 = BY.cat_eq(x, E.cat(y, m))
  +e2 = Equal.cong(List<&2, U32>, List<&2, U32>, z => SE.cat(x, z), E.cat(y, m), SE.cat(y, m), BY.cat_eq(y, m))
  +e3 = Equal.cong(List<&2, U32>, List<&2, U32>, z => SE.cat(z, SE.cat(y, m)), x, sx, ex)
  +e4 = Equal.cong(List<&2, U32>, List<&2, U32>, z => SE.cat(sx, SE.cat(z, m)), y, sy, ey)
  Equal.trans(List<&2, U32>, E.cat(x, E.cat(y, m)), SE.cat(x, E.cat(y, m)), SE.cat(sx, SE.cat(sy, m)), e1, Equal.trans(List<&2, U32>, SE.cat(x, E.cat(y, m)), SE.cat(x, SE.cat(y, m)), SE.cat(sx, SE.cat(sy, m)), e2, Equal.trans(List<&2, U32>, SE.cat(x, SE.cat(y, m)), SE.cat(sx, SE.cat(y, m)), SE.cat(sx, SE.cat(sy, m)), e3, e4)))

Uses (7):
  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.trans
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=List
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=U32
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/ed25519/bytes.bend&name=cat_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/ed25519.bend&name=cat
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/ed25519/ed25519.bend&name=cat