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Proof step 37 from proof four-square-odd-ls (previous step)

(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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ i ^2 < j ^2 ↔ abs(i) < abs(j)

Rule argument

spec: int-square inst: name: two-ls seq: ⊦ i ^2 < j ^2 ↔ abs(i) < abs(j) subst: [j, i] → [i3, j] flags: rewrite

Additional information

Used simplifier rules: abs-16: ⊦ 0 < j → abs(j) = j; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i3, j