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Proof step 23 from proof two-even (previous step)

⊦ j2 ^2 + 2 * j0 * j0 + 2 * j0 * j2 = j0 ^2 + (j2 + j0)^2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2

Rule argument

spec: <toplevel> name: two-plus seq: ⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2 subst: [j, i] → [j0, j2] flags: <all paths>

Additional information

Used simplifier rules: neq: ⊦ j ^2 = j * j ↔ true;% ⊦ i + i = 2 * i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i + j = i + i0 ↔ j = i0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ 0 < i → (i * j = i * j0 ↔ j = j0); (s) Used terms: j0, j2