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Proof step 1 from proof eq-zero (conclusion)

⊦ mkDecimal(i, j) = mkDecimal(0, j0) ↔ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: equality-any seq: ⊦ mkDecimal(i, j) = mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j) subst: [j0, i0, j, i] → [j0, 0, j, i] flags: rewrite, current

Additional information

Used simplifier rules: Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%zero-eq: ⊦ i * j = 0 ↔ i = 0 ∨ j = 0; from specification int-mult%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%absls: ⊦ ¬ abs(i) < 0; from specification int-abs Used terms: j0, 0, j, i