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Proof step 5 from proof four-square-le-zero (previous step)

0 ≤ i ^2, i0 ^2 + i1 ^2 + i2 ^2 ≤ 0, i ^2 + i0 ^2 + i1 ^2 + i2 ^2 ≤ 0 ⊦ i = 0 ∧ i0 = 0 ∧ i1 = 0 ∧ i2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 0 ≤ i ∧ ¬ i0 ≤ j → ¬ i + i0 ≤ j
Proof step 7:
¬(0 ≤ i0 ^2 ∧ ¬ i1 ^2 + i2 ^2 ≤ 0), 0 ≤ i ^2, i0 ^2 + i1 ^2 + i2 ^2 ≤ 0, i ^2 + i0 ^2 + i1 ^2 + i2 ^2 ≤ 0 ⊦ i = 0 ∧ i0 = 0 ∧ i1 = 0 ∧ i2 = 0

Rule argument

spec: int-abs inst: name: notle-pos seq: ⊦ 0 ≤ i ∧ ¬ i0 ≤ j → ¬ i + i0 ≤ j subst: [j, i0, i] → [0, i1 ^2 + i2 ^2, i0 ^2] flags: rewrite

Additional information

Used terms: 0, i1 ^2 + i2 ^2, i0 ^2