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Proof step 8 from proof lagrange-primedivisors (previous step)

Π ints0 = i0 ^2 + i1 ^2 + i2 ^2 + i3 ^2, ∀ 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

User applied rule all left

And obtained the following new goals

Proof step 9:
Π ints0 = i0 ^2 + i1 ^2 + i2 ^2 + i3 ^2, i = i ∨ i ∈ ints0 → (∃ i3, i0, i1, i2. i = i3 ^2 + i0 ^2 + i1 ^2 + i2 ^2), ∀ j0. 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

Rule argument

pos: left 2 terms: i abort: F discard: F computed: T

Additional information

Used terms: i