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Proof step 3 from proof mult-ls (previous step)

dec = mkDecimal(i, i0), mkDecimal(0, 0) < dec ⊦ dec * dec_i < dec * dec_j ↔ dec_i < dec_j

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
0 < i ⊦ mkDecimal(i, i0) * dec_i < mkDecimal(i, i0) * dec_j ↔ dec_i < dec_j

Rule argument

Additional information

Used simplifier rules: ls-zero: ⊦ mkDecimal(0, 0) < mkDecimal(i, j) ↔ 0 < i;%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs