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

Rule argument

Additional information

Used simplifier rules: two-plus: ⊦ (i + j)^2 = i ^2 + 2 * i * j + j ^2;%numlslsdel-01: i0 ≠ 0, i0 < i ⊦ (* i) < j → (* i0) < j; from specification int-basic1%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%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%add-c: ⊦ i + j = j + i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%succ-01: ⊦ i +1 = i + 1; from specification int-basic2