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Proof step 8 from proof root-is-irrational (previous step)

rational(i * i, j0 * j0) = rational(j, 1), gcd(i, j0) = 1, 0 < j0 ⊦ j0 = 0, ∃ i. j = i * i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ 0 < j ∧ 0 < j0 → (rational(i, j) = rational(i0, j0) ↔ i * j0 = i0 * j)
Proof step 10:
0 < j0 * j0 ∧ 0 < 1, (i * i) * 1 = j * j0 * j0, gcd(i, j0) = 1, 0 < j0 ⊦ j0 = 0, ∃ i. j = i * i

Rule argument

name: equality-def rotate: F subst: [j0, i0, j, i] → [1, j, j0 * j0, i * i]

Additional information

Used simplifier rules: ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i; Used terms: 1, j, j0 * j0, i * i