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Proof step 14 from proof test-div-02 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 16:
¬(25 % 10 = 0 ∧ 1 ≠ 0 ∧ 25 ≠ 0), div(mkDecimal(5, 0), mkDecimal(2, 0), 0) * mkDecimal(2, 0) = mkDecimal(5, 0) ⊦ mkDecimal(25 * mkDecimal(2, 0).int, mkDecimal(25, 1).scale + mkDecimal(2, 0).scale) = mkDecimal(5, 0), div(mkDecimal(5, 0), mkDecimal(2, 0), 0) = mkDecimal(25, 1)

Rule argument

spec: decimal inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i subst: [j, i] → [1, 25] flags: rewrite

Additional information

Used terms: 1, 25