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Proof step 16 from proof square-nls (previous step)

j * (j + 1) = i0 * 2 + j0, j0 < 2, i0 < j, 0 ≤ j, 0 ≤ j0, 0 ≤ i0, 0 < j, (i0 + 1) * 2 ≤ i0 * 2 + j0 ⊦

User applied rule cut formula

And closed the goal!

Rule argument

fma: j0 = 0

Additional information

Used simplifier rules: lstwo-01: ⊦ i ≠ 0 ∧ 0 ≤ i → (i < 2 ↔ i = 1); from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%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%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%numle-10: ⊦ 0 < i → ((* i) * j ≤ (* i) * j0 ↔ j ≤ j0); from specification int-mult%succ-01: ⊦ i + 1 ≤ j ↔ i < j; from specification int-abs%irref: ⊦ ¬ i < i; from specification int-basic1 Used formulas: j0 = 0