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Proof step 11 from proof nummult-le-01 (previous step)

abs(j0) < i, 0 < i, j0 < i, i * (i1 + 1) + j0 < i, j0 ≤ 0, i * (i1 + 1) + j0 ≤ 0 ⊦ i * i0 < i * (i1 + 1) + j0 ↔ i0 ≤ i1, i = i * (i1 + 1) + j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ i ≤ j ↔ ¬ j < i
Proof step 13:
i * (i1 + 1) + j0 < i, j0 < i, 0 < i, abs(j0) < i, i * (i1 + 1) + j0 ≤ 0, j0 ≤ 0 ⊦ i * i0 < i * (i1 + 1) + j0 ↔ ¬ i1 < i0, i = i * (i1 + 1) + j0

Rule argument

spec: int-abs name: le-def seq: ⊦ i ≤ j ↔ ¬ j < i subst: [j, i] → [i1, i0] flags: <all paths>

Additional information

Used terms: i1, i0