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Proof step 12 from proof square-not-neg-05 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ i ^2 = i * i

Rule argument

spec: <toplevel> name: Square-def seq: ⊦ i ^2 = i * i subst: [i] → [1] flags: <all paths>

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: 1