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Proof step 9 from proof mod-zero-one (previous step)

i0 % j + i % j < j + j, i % j < j, i0 % j < j, 0 ≤ i, 0 ≤ i0, 0 < j, 1 < (i % j + i0 % j) / j, 0 < (i % j + i0 % j) / j ⊦ (i % j + i0 % j) / j = 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ i + i = 2 * i
Proof step 11:
i0 % j + i % j < 2 * j, i % j < j, i0 % j < j, 0 ≤ i, 0 ≤ i0, 0 < j, 1 < (i % j + i0 % j) / j, 0 < (i % j + i0 % j) / j ⊦ (i % j + i0 % j) / j = 1

Rule argument

spec: int-mult inst: name: add-mult-two seq: ⊦ i + i = 2 * i subst: [i] → [j] flags: rewrite

Additional information

Used terms: j