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Proof step 43 from proof add-scale-neq (previous step)

(dec_i.int + dec_j.int) % 10 = 0, maxScale ( (dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) * 10 ^ min(dec_j.scale, dec_i.scale)) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 ≤ dec_j.scale ⊦ 0 ≤ min(dec_j.scale, dec_i.scale), dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(dec_i.scale, dec_j.scale) + maxScale ( (dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale))) * 10 ^ min(dec_j.scale, dec_i.scale)), dec_i.int % 10 = 0, dec_j.int % 10 = 0, 0 ≤ min(dec_j.scale, dec_i.scale) ∧ dec_i.int * 10 ^ (dec_j.scale - min(dec_j.scale, dec_i.scale)) + dec_j.int * 10 ^ (dec_i.scale - min(dec_j.scale, dec_i.scale)) ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information

Used simplifier rules: forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs