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Proof step 6 from proof lagrange-primedivisors (previous step)

∀ j0. j0 = i ∨ j0 ∈ ints0 → (∃ i, i0, i1, i2. j0 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ j ∈ ints0 → (∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2), ∃ i4, i5, i6, i7. i * Π ints0 = i4 ^2 + i5 ^2 + i6 ^2 + i7 ^2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
j ∈ ints0, ∀ j0. j0 = i ∨ j0 ∈ ints0 → (∃ i, i0, i1, i2. j0 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i4, i5, i6, i7. i * Π ints0 = i4 ^2 + i5 ^2 + i6 ^2 + i7 ^2, ∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

Proof step 6 from proof lagrange-primedivisors (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information