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Proof step 47 from proof equality-any (previous step)

i0 * 10 ^ abs(j) = i * 10 ^ abs(j0), abs(j) < abs(j0), ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ i % 10 = 0, i0 % 10 = 0, i = 0, i0 = 0, i = i0 ∧ abs(j) = abs(j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: pot-eq-sub seq: ⊦ 0 < j ∧ 0 ≤ j0 ∧ j0 ≤ j1 → (i * j ^ j0 = i0 * j ^ j1 ↔ i = i0 * j ^ (j1 - j0)) subst: [j1, i0, j0, j, i] → [abs(j0), i, abs(j), 10, i0] flags: rewrite

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: abs(j0), i, abs(j), 10, i0