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Proof step 7 from proof Lagrange-SumOf4Squares-primes (previous step)

prime(i2 ^2 + i1 ^2 + i0 ^2 + i ^2), 1 < i2 ^2 + i1 ^2 + i0 ^2 + i ^2, 0 < i2 ^2 + i1 ^2 + i0 ^2 + i ^2 ⊦ i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = 2, ∃ i6, i5, i4, i3. i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = i6 ^2 + i5 ^2 + i4 ^2 + i3 ^2

Heuristic quantifier closing applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: i2, i1, i0, i

Additional information

Used simplifier rules: add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i2, i1, i0, i