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Proof step 28 from proof add-scale-neq (previous step)

dec_i.int + dec_j.int * 10 ^ (dec_i.scale - dec_j.scale) = 0, (dec_i.int + dec_j.int) % 10 = 0, 0 < dec_j.scale, 1 < dec_i.scale, dec_j.scale < dec_i.scale, 0 ≤ dec_i.scale + dec_j.scale, 0 ≤ dec_i.scale, 0 < dec_i.scale ⊦ dec_j.scale = 0, dec_i.int % 10 = 0, dec_i.scale = dec_j.scale

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [dec_i.scale - dec_j.scale, 10] flags: rewrite

Additional information

Used simplifier rules: sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-zero: ⊦ i + 0 = i; 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%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: dec_i.scale - dec_j.scale, 10