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Proof step 61 from proof pot-root-est (previous step)

2 * i = j * j + j0, j = sqrt(2 * i), 0 < i, 0 ≤ j0, 0 ≤ j, j0 ≤ 2 * j, 1024 ≤ i, 4 ^ (i / 3) ≤ (2 * i) ^ sqrt(2 * i), 0 ≤ i ⊦ 2 * i < j * (j + 1) + 1 * (j + 1)

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i * j + i0 < i * (j + j1) + j0 ↔ i0 < i * j1 + j0; (s)% ⊦ i + i = 2 * i; (s)%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j + 1 ↔ i ≤ j; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i ≤ j → ¬ j < i; (s)