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Proof step 12 from proof maxScale-zero-01 (previous step)

10 ≠ 0 ∧ 10 ^ maxScale(i / 10) ≠ 0, 0 ≤ maxScale(i / 10), ((i / 10) / 10 ^ maxScale(i / 10)) % 10 = 0, i % 10 = 0, ∀ i0. i→n(i0) < i→n(i) → (i0 / 10 ^ maxScale(i0)) % 10 = 0 → i0 = 0 ⊦ i = 0

User applied rule apply induction

And closed the goal!

Rule argument

subst: [i0] → [i / 10]

Additional information

Used simplifier rules: maxScale-not-negt: ⊦ ¬ maxScale(i) < 0;%div-eq-zero-01: ⊦ 0 ≠ j → (i / j = 0 ↔ abs(i) < abs(j)); from specification int-div%div-div: ⊦ j ≠ 0 ∧ j0 ≠ 0 → (i / j) / j0 = i / (j * j0); from specification int-div%mod-zero-05: ⊦ abs(i) < j → i % j = i; from specification int-div%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%labs: ⊦ i→n(i) < i→n(j) ↔ abs(i) < abs(j); from specification intnat%abs: j ≠ 0 ⊦ abs(i / j) = abs(i) / abs(j); from specification int-div%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%abs-div10-le: ⊦ abs(i) ≤ abs(i) / 10 ↔ i = 0; from specification int-div Used terms: i / 10