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Proof step 12 from proof square-inject (previous step)

(i0 + j0) * (i0 + j0 + 1) = i1 * 2 + j1, (i + j) * (i + j + 1) = (i1 + j0 - j) * 2 + j2, 0 ≤ j2, j1 < 2, 0 ≤ i, 0 ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j1, 0 ≤ i1, j2 < 2, j ≤ i1 + j0, 0 ≤ i1 + j0 ⊦ i = i0 ∧ j = j0

User applied rule cut formula

And obtained the following new goals

Proof step 13:
(i0 + j0) * (i0 + j0 + 1) = i1 * 2 + j1, (i + j) * (i + j + 1) = (i1 + j0 - j) * 2 + j2, 0 ≤ j2, j1 < 2, 0 ≤ i, 0 ≤ j, 0 ≤ i0, 0 ≤ j0, 0 ≤ j1, 0 ≤ i1, j2 < 2, j ≤ i1 + j0, 0 ≤ i1 + j0 ⊦ j1 = 1, i = i0 ∧ j = j0

Rule argument

fma: j1 = 1

Additional information

Used simplifier rules: square-even: ⊦ i * (i + 1) ≠ 2 * j + 1; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: j1 = 1