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Proof step 74 from proof add-scale-neq (previous step)

min(dec_j.scale, dec_i.scale) ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_j.scale, 0 ≤ dec_i.scale ⊦ (dec_i.int + dec_j.int) % 10 = 0, dec_j.int % 10 = 0, dec_i.int % 10 = 0, dec_i.scale = dec_j.scale, dec_i.scale + dec_j.scale = max(dec_i.scale, dec_j.scale) + min(dec_j.scale, dec_i.scale)

User applied rule insert rewrite lemma

And obtained the following new goals

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%Max-right: ⊦ j < i → max(j, i) = i; 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%add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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