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Proof step 23 from proof square-scale (previous step)

∀ i1, i0. i→n(i1) < i→n(j * 10) → true → even(mkDecimal(i1 * i1, 2 * abs(i0)).scale) ⊦ i0 = 0, j = 0, even(mkDecimal(j * j, 2 * abs(i0) - 2).scale)

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [i1, i0] → [j, abs(i0) - 1]

Additional information

Used simplifier rules: labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat%abs-eqall: ⊦ abs(i * j) = abs(i) * abs(j); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%le-same-04: ⊦ i * abs(j) ≤ abs(j) ↔ j = 0 ∨ i ≤ 1; from specification int-mult Used terms: j, abs(i0) - 1