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Proof step 1 from proof ex-modeq-half-all (conclusion)

0 < j0, odd(j0), i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j ⊦ ∃ i3, i4, i5, i6. ≡mod(i3, i, j0) ∧ abs(i3) ≤ j0 / 2 ∧ ≡mod(i4, i0, j0) ∧ abs(i4) ≤ j0 / 2 ∧ ≡mod(i5, i1, j0) ∧ abs(i5) ≤ j0 / 2 ∧ ≡mod(i6, i2, j0) ∧ abs(i6) ≤ j0 / 2

User applied rule insert lemma

And obtained the following new goals

Proof step 2:
0 < j ∧ odd(j) ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2
Proof step 3:
∃ i1. ≡mod(i1, i, j0) ∧ abs(i1) ≤ j0 / 2, 0 < j0, odd(j0), i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j ⊦ ∃ i3, i4, i5, i6. ≡mod(i3, i, j0) ∧ abs(i3) ≤ j0 / 2 ∧ ≡mod(i4, i0, j0) ∧ abs(i4) ≤ j0 / 2 ∧ ≡mod(i5, i1, j0) ∧ abs(i5) ≤ j0 / 2 ∧ ≡mod(i6, i2, j0) ∧ abs(i6) ≤ j0 / 2

Rule argument

spec: inst: name: ex-modeq-half seq: 0 < j ∧ odd(j) ⊦ ∃ i. ≡mod(i, i0, j) ∧ abs(i) ≤ j / 2 subst: [j, i0] → [j0, i] flags: current, []

Additional information

Used terms: j0, i