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Proof step 50 from proof two-even (previous step)

2 * i = ((2 * i1 + 1) + j2)^2 + j2 ^2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2
Proof step 52:
2 * i = ((2 * i1 + 1)^2 + 2 * (2 * i1 + 1) * j2 + j2 ^2) + j2 ^2 ⊦ i = ((2 * i1 + 1) / 2)^2 + ((2 * j2 + 2 * i1 + 1) / 2)^2

Rule argument

spec: inst: name: two-plus seq: ⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2 subst: [j, i] → [j2, 2 * i1 + 1] flags: rewrite, current

Additional information

Used terms: j2, 2 * i1 + 1