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Proof step 36 from proof four-square-odd-ls (previous step)

i4 ^2 ≤ j ^2 ∧ i5 ^2 + i6 ^2 ≤ j ^2 + j ^2, ¬ i3 ^2 ≤ j ^2 ∨ ¬ true, (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 ⊦ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ≤ j ^2 + j ^2 + j ^2 + j ^2, j = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
(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, i4 ^2 ≤ j ^2, i5 ^2 + i6 ^2 ≤ 2 * j ^2, 4 * j ^2 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, j ^2 < i3 ^2, i4 ^2 < i3 ^2 ⊦ j = 0

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult