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Proof step 8 from proof dec2int-def-any (previous step)

∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ mkDecimal(i, j).int / 10 ^ mkDecimal(i, j).scale = i / 10 ^ abs(j), i % 10 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 10:
¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0), ∀ i0, j. i→n(i0) < i→n(i) → true → dec2int(mkDecimal(i0, j)) = i0 / 10 ^ abs(j) ⊦ i / 10 ^ mkDecimal(i, j).scale = i / 10 ^ abs(j), i % 10 = 0, j = 0

Rule argument

spec: inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i