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Proof step 6 from proof modeqp (previous step)

(j * i1 + j) + j0 = i0 * j + j1, j0 < j, j1 < j, 0 < j, 0 ≤ j0, 0 ≤ j1, i1 * j + j0 = (i0 - 1) * j + j1 → i0 = i1 + 1 ∧ j0 = j1 ⊦ i1 + 1 = i0 ∧ j0 = j1

Heuristic elimination applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i0, 1, i] flags:

Additional information

Used simplifier rules: dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2% ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i0, 1, i