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Proof step 23 from proof test-div-02 (previous step)

div(mkDecimal(5, 0), mkDecimal(2, 0), 0) * mkDecimal(2, 0) = mkDecimal(5, 0) ⊦ div(mkDecimal(5, 0), mkDecimal(2, 0), 0) = mkDecimal(25, 1), mkDecimal(50, 1 + mkDecimal(2, 0).scale) = mkDecimal(5, 0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)
Proof step 25:
¬(2 % 10 = 0 ∧ 0 ≠ 0 ∧ 2 ≠ 0), div(mkDecimal(5, 0), mkDecimal(2, 0), 0) * mkDecimal(2, 0) = mkDecimal(5, 0) ⊦ div(mkDecimal(5, 0), mkDecimal(2, 0), 0) = mkDecimal(25, 1), mkDecimal(50, 1 + abs(0)) = mkDecimal(5, 0)

Rule argument

spec: decimal inst: name: scale-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j) subst: [j, i] → [0, 2] flags: rewrite

Additional information

Used terms: 0, 2