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Proof step 8 from proof square-not-neg-05 (previous step)

sqrt(i) = 0, 0 ^2 < (j + 1) * (j + 1), 0 ≤ i, j * j < 0 ^2 + 1 ^2, 1 < 0 ^2 + 1 ^2, i < 0 ^2 + 1 ^2, 0 ^2 ≤ i, 0 < j, 1 < (j + 1) * (j + 1), 0 < (j + 1) * (j + 1), i < (j + 1) * (j + 1), j * j ≤ i, 0 < i, 0 < 0 ^2 + 1 ^2, 0 < 1 ^2 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i ^2 = i * i
Proof step 10:
sqrt(i) = 0, 0 * 0 < (j + 1) * (j + 1), 0 ≤ i, j * j < 0 * 0 + 1 ^2, 1 < 0 * 0 + 1 ^2, i < 0 * 0 + 1 ^2, 0 * 0 ≤ i, 0 < j, 1 < (j + 1) * (j + 1), 0 < (j + 1) * (j + 1), i < (j + 1) * (j + 1), j * j ≤ i, 0 < i, 0 < 0 * 0 + 1 ^2, 0 < 1 ^2 ⊦

Rule argument

spec: inst: name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [0] flags: rewrite, current

Additional information

Used terms: 0