Index.lane_eq: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/index.bend as Index
Lines 84-87 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/index.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/index.bend&start_line=84&end_line=87

import Base
import bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/types.bend as T
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/types.bend as A
import bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/argon2.bend as I
import bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/blamka.bend as SG

def lane_eq(+b: A.Block, +n: Nat) -> {I.lane(b, n) == SG.lane(b, n) : T.Lane}:
  Equal.trans(T.Lane, I.at(I.row_at(b, Nat.div(n, 16n)), Nat.mod(n, 16n)), I.at(SG.row(b, Nat.div(n, 16n)), Nat.mod(n, 16n)), SG.lane(b, n),
    Equal.cong(T.State, T.Lane, z => I.at(z, Nat.mod(n, 16n)), I.row_at(b, Nat.div(n, 16n)), SG.row(b, Nat.div(n, 16n)), row_at_eq(b, Nat.div(n, 16n))),
    at_eq(SG.row(b, Nat.div(n, 16n)), Nat.mod(n, 16n)))

Uses (15):
  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=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.div
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.mod
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/index.bend&name=at_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/argon2/index.bend&name=row_at_eq
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/blamka.bend&name=lane
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/crypto/argon2/blamka.bend&name=row
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/argon2.bend&name=at
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/argon2.bend&name=lane
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/argon2.bend&name=row_at
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/argon2/types.bend&name=Block
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/types.bend&name=Lane
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/src/crypto/blake/blake2b/types.bend&name=State