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Proof step 79 from proof getsetShort-theorem (previous step)

j % 256 = 0, j / 256 ≤ 127, ~128 ≤ j / 256, b2i(i2b(j)) < 256, ~32768 ≤ j, j < 0, 0 < b2i(i2b(j)) ⊦ b2i(i2b(j)) = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 80:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

Rule argument

spec: int-div inst: name: modex seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [256, j] flags: rewrite

Additional information

Used simplifier rules: byte-mult: ⊦ i2b(i * 256) = i2b(0);%byte: ⊦ b2i(i2b(0)) = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 256, j