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Proof step 9 from proof four-square-odd-ls (previous step)

i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ≤ j ^2 + j ^2 + j ^2 + j ^2, (2 * j + 1)^2 ≤ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0 < j, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, abs(i3) ≤ j, abs(i4) ≤ j, abs(i5) ≤ j, abs(i6) ≤ j ⊦ j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
(2 * j + 1)^2 ≤ 4 * j ^2, i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ≤ 4 * j ^2, abs(i6) ≤ j, abs(i5) ≤ j, abs(i4) ≤ j, abs(i3) ≤ j, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0 < j, (2 * j + 1)^2 ≤ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0 < j ^2 ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le: ⊦ i ≤ j ∧ 0 < i → 0 < j; (forward) from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult