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Proof step 51 from proof pot-root-est (previous step)

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

User applied rule insert equation

And closed the goal!

Rule argument

pos: left 1 flags: discard

Additional information

Used simplifier rules: ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i + j < j ↔ i < 0; (s)% ⊦ i ≤ j → ¬ j < i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2