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Proof step 1 from proof less-def-any (conclusion)

⊦ mkDecimal(i, j) < mkDecimal(i0, j0) ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ dec_i < dec_j ↔ (dec_i - dec_j).int < 0
Proof step 3:
⊦ (mkDecimal(i, j) - mkDecimal(i0, j0)).int < 0 ↔ i * 10 ^ abs(j0) < i0 * 10 ^ abs(j)

Rule argument

spec: inst: name: ls-def seq: ⊦ dec_i < dec_j ↔ (dec_i - dec_j).int < 0 subst: [dec_j, dec_i] → [mkDecimal(i0, j0), mkDecimal(i, j)] flags: rewrite, current

Additional information

Used terms: mkDecimal(i0, j0), mkDecimal(i, j)