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Proof step 2 from proof even-sum (previous step)

even(i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i3, i4, i5, i6. even(i3 + i4) ∧ even(i5 + i6) ∧ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

User applied rule cut formula

And obtained the following new goals

Proof step 3:
i ^2 + i0 ^2 + i1 ^2 + i2 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2, even(i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i3, i4, i5, i6. even(i3 + i4) ∧ even(i5 + i6) ∧ i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Rule argument

fma: i ^2 + i0 ^2 + i1 ^2 + i2 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2

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 formulas: i ^2 + i0 ^2 + i1 ^2 + i2 ^2 = (i ^2 + i0 ^2) + i1 ^2 + i2 ^2