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Proof step 64 from proof equality-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ j0 = 0, mkDecimal(i, j) = mkDecimal(0, abs(j0) - 1) ↔ i * 10 ^ abs(j0) = 0, i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 65:
⊦ mkDecimal(0, j) = mkDecimal(0, 0)
Proof step 66:
∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ j0 = 0, mkDecimal(i, j) = mkDecimal(0, 0) ↔ i * 10 ^ abs(j0) = 0, i % 10 = 0 ∧ j ≠ 0

Rule argument

spec: inst: name: mkDecimal-zero seq: ⊦ mkDecimal(0, j) = mkDecimal(0, 0) subst: [j] → [abs(j0) - 1] flags: rewrite, current

Additional information

Used terms: abs(j0) - 1