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Proof step 2 from proof four-square-congmod (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i3, i2, j0), ≡mod(i4, i1, j0), ≡mod(i5, i0, j0), ≡mod(i6, i, j0), 1 < j, 0 < j, 0 < j0, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ⊦ j0 = 1, j = 2, ≡mod(i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2, 0, j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 4:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i3, i2, j0), ≡mod(i4, i1, j0), ≡mod(i5, i0, j0), ≡mod(i6, i, j0), 1 < j, 0 < j, 0 < j0, 0 < i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 ⊦ j0 = 1, j = 2, j0 | abs(i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2 - 0)

Rule argument

spec: inst: name: congmod-def seq: ⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0) subst: [j, i0, i] → [j0, 0, i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2] flags: rewrite, current

Additional information

Used terms: j0, 0, i3 ^2 + i4 ^2 + i5 ^2 + i6 ^2