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Proof step 10 from proof four-square-le-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
i0 ^2 + i2 ^2 ≤ 0, i ^2 + i0 ^2 + i2 ^2 ≤ 0, i ^2 + i2 ^2 ≤ 0, i2 ^2 ≤ 0, 0 ≤ i1 ^2, 0 ≤ i ^2, i0 ^2 + i1 ^2 + i2 ^2 ≤ 0, i ^2 + i0 ^2 + i1 ^2 + i2 ^2 ≤ 0, 0 ≤ i0 ^2, i1 ^2 + i2 ^2 ≤ 0, i ^2 + i1 ^2 + i2 ^2 ≤ 0 ⊦ i = 0 ∧ i0 = 0 ∧ i1 = 0 ∧ i2 = 0

Rule argument

Additional information

Used simplifier rules: two-not-neg: ⊦ ¬ i ^2 < 0;%lep-01: ⊦ i + j ≤ i ↔ j ≤ 0; from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%forward-lele: ⊦ j ≤ j0 ∧ j0 ≤ j1 → j ≤ j1; (forward) from specification int-abs%forward-le-04: ⊦ j ≤ i ∧ i ≤ 0 → j ≤ 0; (forward) from specification int-abs%forward-le-01: ⊦ 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%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs