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Proof step 1 from proof less-same (conclusion)

⊦ mkDecimal(i, j) < mkDecimal(i0, j) ↔ i < i0

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

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, j), mkDecimal(i, j)] flags: rewrite, current

Additional information

Used simplifier rules: sub-same: ⊦ mkDecimal(i, j) - mkDecimal(i0, j) = mkDecimal(i - i0, j);%getint-neg-02: ⊦ mkDecimal(i, j).int < 0 ↔ i < 0; from specification decimal%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: mkDecimal(i0, j), mkDecimal(i, j)