Value.sh3: def of bend-collections-laws-crypto@1.0.0.0
Import: import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend as Value
Lines 326-330 of bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend: https://jend.leeeet.dev/read.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/value.bend&start_line=326&end_line=330

import Base
import bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend as C
import bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend as N
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend as WW
import bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend as WM
import bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend as A

# (a + 2^8 b) + 2^8 c == a + 2^8 (b + c)
def sh3(+a: Nat, +b: Nat, +c: Nat) -> {Nat.add(Nat.add(a, C.shift(8n, b)), C.shift(8n, c)) == Nat.add(a, C.shift(8n, Nat.add(b, c))) : Nat}:
  A.tr(Nat.add(Nat.add(a, C.shift(8n, b)), C.shift(8n, c)), Nat.add(a, Nat.add(C.shift(8n, b), C.shift(8n, c))), Nat.add(a, C.shift(8n, Nat.add(b, c))),
    N.add_assoc(a, C.shift(8n, b), C.shift(8n, c)),
    WM.cong_r(a, Nat.add(C.shift(8n, b), C.shift(8n, c)), C.shift(8n, Nat.add(b, c)), A.sy(C.shift(8n, Nat.add(b, c)), Nat.add(C.shift(8n, b), C.shift(8n, c)), WW.shift_add(8n, b, c))))

Uses (8):
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat
  https://jend.leeeet.dev/definition.txt?path=Base/base.bend&name=Nat.add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=sy
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/crypto/poly1305/arith.bend&name=tr
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/lib/nat.bend&name=add_assoc
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/w64mul.bend&name=cong_r
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/proofs/math/typed/width.bend&name=shift_add
  https://jend.leeeet.dev/definition.txt?path=bend-collections-laws-crypto@1.0.0.0/spec/lib/common.bend&name=shift