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Proof step 2 from proof modeqp (previous step)

i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j, 0 < j ⊦ i = i0 ∧ j0 = j1

User applied rule structural induction

And obtained the following new goals

Rule argument

indvar: i

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%ls-add: ⊦ 0 ≤ j1 ∧ j1 < j → (i0 * j + j1 < j ↔ i0 ≤ 0);%zero-ge-add: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0);%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0;%int generated by 0, +1, -1;;%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lf-03: ⊦ i < j ∧ i = i0 → i0 < j; (forward) from specification int-basic1%anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%eq: ⊦ i = i + j ↔ j = 0; from specification int-basic2