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Proof step 6 from proof even-sum (previous step)

even(i ^2 + i0 ^2) ∧ even(i1 ^2 + i2 ^2) ∨ odd(i ^2 + i0 ^2) ∧ odd(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 insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ even(i + j) ↔ even(i) ∧ even(j) ∨ odd(i) ∧ odd(j)
Proof step 8:
(even(i ^2) ∧ even(i0 ^2) ∨ odd(i ^2) ∧ odd(i0 ^2)) ∧ even(i1 ^2 + i2 ^2) ∨ odd(i ^2 + i0 ^2) ∧ odd(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

spec: int-min inst: name: even-add seq: ⊦ even(i + j) ↔ even(i) ∧ even(j) ∨ odd(i) ∧ odd(j) subst: [j, i] → [i0 ^2, i ^2] flags: rewrite

Additional information

Used terms: i0 ^2, i ^2