x = (x n)n+(x mod n)

y = (y n)n+(y mod n)

(x mod n)(y mod n) = (((x mod n)(y mod n)) n)n+(((x mod n)(y mod n)) mod n)

(((x mod n)(y mod n)) mod n) < n

((xy) mod n) = (((x mod n)(y mod n)) mod n)

Inst Thm* a:, n:, q:, r:. a = qn+r r < n q = (a n) & r = (a mod n) [xy;n;(x n)(y n)n+(x n)(y mod n)+(x mod n)(y n)+(((x mod n)(y mod n)) n);((x mod n)(y mod n)) mod n]

1

xy = ((x n)(y n)n+(x n)(y mod n)+(x mod n)(y n)+(((x mod n)(y mod n)) n))n+(((x mod n)(y mod n)) mod n)

1 step

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