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Proof step 52 from proof four-square-congmod (previous step)

i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, 0 < (j0 ^2 * i6 ^2 + 2 * (j0 * i6) * i2 + i2 ^2) + (j0 ^2 * i3 ^2 + 2 * (j0 * i3) * i1 + i1 ^2) + (j0 ^2 * i7 ^2 + 2 * (j0 * i7) * i0 + i0 ^2) + j0 ^2 * i5 ^2 + 2 * (j0 * i5) * i + i ^2 ⊦ j0 = 1, j = 2, j0 | j0 ^2 * i6 ^2 + i2 ^2 + j0 ^2 * i3 ^2 + i1 ^2 + j0 ^2 * i7 ^2 + i0 ^2 + j0 ^2 * i5 ^2 + i ^2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-square inst: name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [j0] flags: rewrite

Additional information

Used simplifier rules: divides-mult-add: ⊦ i | i * j + j0 ↔ i | j0; from specification int-gcd%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%div-mult: ⊦ i | i * j; from specification int-gcd Used terms: j0