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Proof step 4 from proof add-pos (previous step)

mkDecimal(0, 0) ≤ dec_j, mkDecimal(0, 0) ≤ dec_i ⊦ ¬ dec_i + dec_j < mkDecimal(0, 0)

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ls-le-trans: ⊦ dec < dec0 ∧ dec0 ≤ dec1 → dec < dec1;%ls-add-02: ⊦ dec_i + dec_j < dec_j ↔ dec_i < mkDecimal(0, 0);%add-a: ⊦ dec0 + dec1 + dec2 = (dec0 + dec1) + dec2;%add-c: ⊦ dec_i + dec_j = dec_j + dec_i;%le-ls-trans: ⊦ dec ≤ dec0 ∧ dec0 < dec1 → dec < dec1;%less-irref: ⊦ ¬ dec < dec;