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Proof step 1 from proof lagrange-primedivisors (conclusion)

∀ j. j ∈ ints → (∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i, i0, i1, i2. Π ints = i ^2 + i0 ^2 + i1 ^2 + i2 ^2

User applied rule structural induction

And obtained the following new goals

Proof step 2:
∀ j. j ∈ [] → (∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i, i0, i1, i2. Π [] = i ^2 + i0 ^2 + i1 ^2 + i2 ^2
Proof step 4:
(∀ j. j ∈ ints0 → (∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2)) → (∃ i, i0, i1, i2. Π ints0 = i ^2 + i0 ^2 + i1 ^2 + i2 ^2), ∀ j. j ∈ i + ints0 → (∃ i, i0, i1, i2. j = i ^2 + i0 ^2 + i1 ^2 + i2 ^2) ⊦ ∃ i3, i0, i1, i2. Π(i + ints0) = i3 ^2 + i0 ^2 + i1 ^2 + i2 ^2

Rule argument

indvar: ints

Additional information

Used simplifier rules: intlist freely generated by [], +;;