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Proof step 3 from proof square-four (previous step)

0 ≤ 4 → sqrt(4) ^2 ≤ 4 ∧ 4 < sqrt(4) +1 ^2 ⊦ sqrt(4) = 2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
4 < (sqrt(4) + 1)^2, sqrt(4) ^2 < (sqrt(4) + 1)^2, 0 < (sqrt(4) + 1)^2, 1 < (sqrt(4) + 1)^2, sqrt(4) ^2 ≤ 4 ⊦ sqrt(4) = 2

Rule argument

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-pos: ⊦ i < j ∧ 0 < i → 0 < j ∧ 1 < j; (forward) from specification int-basic1% ⊦ i +1 = i + 1; (s)