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Proof step 20 from proof dec2int-def-any (previous step)

dec2int(mkDecimal(j0, abs(j) - 1)) = j0 / 10 ^ (abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(j0 * 10) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ j = 0, j0 / 10 ^ (abs(j) - 1) = (j0 * 10) / 10 ^ abs(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ 0 < i → j ^ i = j ^ i -1 * j

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [abs(j), 10] flags: rewrite

Additional information

Used simplifier rules: sub-pred: ⊦ i -1 = i - 1; from specification int-abs%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%abs-10: ⊦ abs(i) - 1 < 0 ↔ i = 0; from specification int-abs%div-mult-01: j ≠ 0, i0 ≠ 0 ⊦ (i * i0) / (j * i0) = i / j; from specification int-div%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs Used terms: abs(j), 10