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Proof step 38 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 * i6)^2 + 2 * (j0 * i6) * i2 + i2 ^2) + ((j0 * i3)^2 + 2 * (j0 * i3) * i1 + i1 ^2) + ((j0 * i7)^2 + 2 * (j0 * i7) * i0 + i0 ^2) + (j0 * i5 + i)^2 ⊦ j0 = 1, j = 2, j0 | (j0 * i6)^2 + i2 ^2 + (j0 * i3)^2 + i1 ^2 + (j0 * i7)^2 + i0 ^2 + (j0 * i5 + i)^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 39:
⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2
Proof step 40:
i2 ^2 + i1 ^2 + i0 ^2 + i ^2 = j0 * j, 1 < j, 0 < j, 0 < j0, 0 < ((j0 * i6)^2 + 2 * (j0 * i6) * i2 + i2 ^2) + ((j0 * i3)^2 + 2 * (j0 * i3) * i1 + i1 ^2) + ((j0 * i7)^2 + 2 * (j0 * i7) * i0 + i0 ^2) + (j0 * i5)^2 + 2 * (j0 * i5) * i + i ^2 ⊦ j0 = 1, j = 2, j0 | (j0 * i6)^2 + i2 ^2 + (j0 * i3)^2 + i1 ^2 + (j0 * i7)^2 + i0 ^2 + (j0 * i5)^2 + 2 * (j0 * i5) * i + i ^2

Rule argument

spec: int-square inst: name: two-plus seq: ⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2 subst: [j, i] → [i, j0 * i5] flags: rewrite

Additional information

Used terms: i, j0 * i5