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Proof step 100 from proof add-scale-neq (previous step)

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

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%sub-sub-03: ⊦ i - i = 0; from specification int-abs%one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%scale-not-neg: ⊦ ¬ dec.scale < 0; from specification decimal%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%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs Used terms: dec_i.scale, dec_j.scale