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Proof step 13 from proof four-square-le-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%zero-le: ⊦ 0 < i → (i * j ≤ 0 ↔ j ≤ 0); from specification int-mult%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%numsucc: ⊦ (* i0) * i + i = (i0 + 1) * i; from specification int-mult%add-mult-two: ⊦ i + i = 2 * i; from specification int-mult