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Proof step 6 from proof mod-div-ls (previous step)

i1 ≤ (i1 + i1 * j0) / j, j0 < j, 0 < j, 0 < i1, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, i0 < i1, 0 ≤ j0, 0 ≤ i2, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ i * j + i = i * (j + 1)
Proof step 8:
i1 ≤ (i1 * (j0 + 1)) / j, j0 < j, 0 < j, 0 < i1, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, i0 < i1, 0 ≤ j0, 0 ≤ i2, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j ⊦

Rule argument

spec: int-mult inst: name: succ-rmerge seq: ⊦ i * j + i = i * (j + 1) subst: [j, i] → [j0, i1] flags: rewrite

Additional information

Used simplifier rules: add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: j0, i1