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Proof step 85 from proof add-scale-neq (previous step)

min(dec_j.scale, dec_i.scale) < 0, 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)), 0 ≤ dec_j.scale, 0 ≤ dec_i.scale ⊦ dec_i.scale = dec_j.scale, 0 = max(dec_i.scale, dec_j.scale)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 86:
⊦ ¬ j < i → min(j, i) = i

Rule argument

spec: int-min inst: name: Min-right seq: ⊦ ¬ j < i → min(j, i) = i subst: [i, j] → [dec_i.scale, dec_j.scale] flags: rewrite

Additional information

Used simplifier rules: lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%Max-left: ⊦ ¬ j < i → max(j, i) = j; from specification int-min%max-a: ⊦ max(i, max(j, j0)) = max(max(i, j), j0); from specification int-min%max-c: ⊦ max(i, j) = max(j, i); from specification int-min%scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal%Max-right: ⊦ j < i → max(j, i) = i; from specification int-min%Min-left: ⊦ j < i → min(j, i) = j; from specification int-min%min-a: ⊦ min(i, min(j, j0)) = min(min(i, j), j0); from specification int-min%min-c: ⊦ min(i, j) = min(j, i); from specification int-min Used terms: dec_i.scale, dec_j.scale