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Proof step 11 from proof four-square-congmod (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i4, i1, j0), ≡mod(i3, i2, j0), 0 < j0, 0 < j, 1 < j, ≡mod(i6, i, j0), 0 < i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + i6 ^2 ⊦ j = 2, j0 = 1, j0 | i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + i6 ^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ≡mod(i, i0, j) ↔ j | abs(i - i0)
Proof step 13:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, ≡mod(i4, i1, j0), ≡mod(i3, i2, j0), 0 < j0, 0 < j, 1 < j, j0 | abs(i6 - i), 0 < i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + i6 ^2 ⊦ j = 2, j0 = 1, j0 | i3 ^2 + i4 ^2 + (j0 * i7 + i0)^2 + i6 ^2

Rule argument

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

Additional information

Used terms: j0, i, i6