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Proof step 16 from proof even-sum (previous step)

(even(i) ∧ even(i0) ∨ odd(i) ∧ odd(i0)) ∧ (even(i1) ∧ even(i2) ∨ odd(i1) ∧ odd(i2)) ∨ (odd(i) ∧ even(i0) ∨ even(i) ∧ odd(i0)) ∧ (odd(i1 ^2) ∧ even(i2 ^2) ∨ even(i1 ^2) ∧ odd(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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
(even(i) ∧ even(i0) ∨ odd(i) ∧ odd(i0)) ∧ (even(i1) ∧ even(i2) ∨ odd(i1) ∧ odd(i2)) ∨ (odd(i) ∧ even(i0) ∨ even(i) ∧ odd(i0)) ∧ (odd(i1) ∧ even(i2) ∨ even(i1) ∧ odd(i2)) ⊦ ∃ 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

Additional information

Used simplifier rules: even-square: ⊦ even(i ^2) ↔ even(i); from specification int-pot%odd-square: ⊦ odd(i ^2) ↔ odd(i); from specification int-pot