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Proof step 67 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, 0) ↔ i * 10 ^ abs(j0) = 0, i % 10 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ i * j = 0 ↔ i = 0 ∨ j = 0
Proof step 69:
∀ 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 = 0 ∨ 10 ^ abs(j0) = 0, i % 10 = 0, j = 0

Rule argument

spec: int-mult inst: name: zero-eq seq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0 subst: [j, i] → [10 ^ abs(j0), i] flags: rewrite

Additional information

Used terms: 10 ^ abs(j0), i