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Proof step 8 from proof square-even (previous step)

(2 * j0) * 2 * j0 + 2 * j0 = 2 * j + 1 ⊦

User applied rule apply lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: modeqp seq: i * j + j0 = i0 * j + j1, 0 ≤ j0, j0 < j, 0 ≤ j1, j1 < j ⊦ i = i0 ∧ j0 = j1 subst: [i, j, j0, i0, j1] → [2 * j0 * j0 + j0, 2, 0, j, 1]

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%dist-lsplit: ⊦ (i + i0) * j = i * j + i0 * j;%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + 0 = i; (s) Used terms: 2 * j0 * j0 + j0, 2, 0, j, 1