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Proof step 39 from proof four-square-mod-zero (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 40:
1 < j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3), 0 ≤ i0 * i0 + i2 * i2 + i * i + i3 * i3, 0 < j0, prime(j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3)), 1 < i0 * i0 + i2 * i2 + i * i + i3 * i3, 0 < i0 * i0 + i2 * i2 + i * i + i3 * i3 ⊦ j0 = 1, j0 * (i0 * i0 + i2 * i2 + i * i + i3 * i3) = 2

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-same-01: ⊦ 0 < i → (i < i * j ↔ 1 < j); from specification int-mult%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%zero-ge: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%eq-pos: ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); from specification int-mult