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Proof step 4 from proof root-is-irrational (previous step)

∃ i, j. ri = rational(i, j) ∧ ri.num = i ∧ ri.denom = j ∧ 0 < j ∧ gcd(i, j) = 1, ri * ri = rational(j, 1) ⊦ ∃ i. j = i * i

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
gcd(i, j0) = 1, rational(i, j0) * rational(i, j0) = rational(j, 1), 0 < j0 ⊦ ∃ i. j = i * i

Rule argument

Additional information

Used simplifier rules: num-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).num = i;%denom-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).denom = j;% ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward)