def assoc

import bend-osdev-gf@0.1.1.0/PROOF.bend as PROOF
import Base
import bend-osdev-gf@0.1.1.0/gf.bend as G

1766def assoc(+a: G.Gf8Bits, +b: G.Gf8Bits, +c: G.Gf8Bits, +p: G.Gf8Bits) -> {G.Gf8Bits.mul(G.Gf8Bits.mul(a, b, p), c, p) == G.Gf8Bits.mul(a, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}:
1767  %dec(a) : {G.Gf8Bits.mul(G.Gf8Bits.mul(_, b, p), c, p) == G.Gf8Bits.mul(a, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}
1768  %dec(a) : {G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p) == G.Gf8Bits.mul(_, G.Gf8Bits.mul(b, c, p), p) : G.Gf8Bits}
1769  Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(G.Gf8Bits.mul(ss(bl(a), basis()), b, p), c, p), G.Gf8Bits.mul(ss(bl(a), ml(basis(), b, p)), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.cong(G.Gf8Bits, G.Gf8Bits, z => G.Gf8Bits.mul(z, c, p), G.Gf8Bits.mul(ss(bl(a), basis()), b, p), ss(bl(a), ml(basis(), b, p)), lin_l(bl(a), basis(), b, p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), ml(basis(), b, p)), c, p), G.Gf8Bits.mul(ss(bl(a), xs(b, p)), c, p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => G.Gf8Bits.mul(ss(bl(a), l), c, p), ml(basis(), b, p), xs(b, p), ml_x(b, p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), xs(b, p)), c, p), ss(bl(a), ml(xs(b, p), c, p)), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), lin_l(bl(a), xs(b, p), c, p), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => ss(bl(a), l), ml(xs(b, p), c, p), xs(G.Gf8Bits.mul(b, c, p), p), mlx_c(b, c, p))))), Equal.sym(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), Equal.trans(G.Gf8Bits, G.Gf8Bits.mul(ss(bl(a), basis()), G.Gf8Bits.mul(b, c, p), p), ss(bl(a), ml(basis(), G.Gf8Bits.mul(b, c, p), p)), ss(bl(a), xs(G.Gf8Bits.mul(b, c, p), p)), lin_l(bl(a), basis(), G.Gf8Bits.mul(b, c, p), p), Equal.cong(List<&2, G.Gf8Bits>, G.Gf8Bits, l => ss(bl(a), l), ml(basis(), G.Gf8Bits.mul(b, c, p), p), xs(G.Gf8Bits.mul(b, c, p), p), ml_x(G.Gf8Bits.mul(b, c, p), p)))))
Uses (15)

Used by (1)

bend-osdev-gf@0.1.1.0/LAWS:mul_assoc