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Proof step 1 from proof mult-pos-02 (conclusion)

⊦ mkDecimal(0, 0) ≤ dec_i ∧ mkDecimal(0, 0) ≤ dec_j → ¬ dec_i * dec_j < mkDecimal(0, 0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
dec_i * dec_j < mkDecimal(0, 0), mkDecimal(0, 0) ≤ dec_i, mkDecimal(0, 0) ≤ dec_j, dec_i * dec_j < dec_i, dec_i * dec_j < dec_j ⊦

Rule argument

Additional information

Used simplifier rules: ls-le-trans: ⊦ dec < dec0 ∧ dec0 ≤ dec1 → dec < dec1;