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Proof step 10 from proof maxScale-pot10-nls (previous step)

0 < j, maxScale(i * 10 ^ (j - 1)) + 1 < j, ∀ j0, i. i→n(j0) < i→n(j) → maxScale(i * 10 ^ j0) < j0 ∧ 0 ≤ j0 → i = 0 ⊦ i = 0, j = 0

User applied rule apply induction

And closed the goal!

Rule argument

subst: [j0, i] → [j - 1, i]

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%lst-03: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0; from specification int-basic2%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%abs-pred: ⊦ i→n(i - 1) < i→n(i) ↔ 0 < i; from specification intnat%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j - 1, i