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Proof step 37 from proof four-square-mod-zero (previous step)

(j0 * i0) * j0 * i0 + (j0 * i2) * j0 * i2 + (j0 * i) * j0 * i + (j0 * i3) * j0 * i3 = j0 * j, prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j ⊦ j0 = 1, j = 2

User applied rule cut formula

And obtained the following new goals

Proof step 38:
(j0 * i0) * j0 * i0 + (j0 * i2) * j0 * i2 + (j0 * i) * j0 * i + (j0 * i3) * j0 * i3 = j0 * j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3), (j0 * i0) * j0 * i0 + (j0 * i2) * j0 * i2 + (j0 * i) * j0 * i + (j0 * i3) * j0 * i3 = j0 * j, prime(j), j0 < j, 1 < j, 0 < j, 0 < j0, 0 ≤ j ⊦ j0 = 1, j = 2

Rule argument

fma: (j0 * i0) * j0 * i0 + (j0 * i2) * j0 * i2 + (j0 * i) * j0 * i + (j0 * i3) * j0 * i3 = j0 * j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3)

Additional information

Used simplifier rules: eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult%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 Used formulas: (j0 * i0) * j0 * i0 + (j0 * i2) * j0 * i2 + (j0 * i) * j0 * i + (j0 * i3) * j0 * i3 = j0 * j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3)