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Proof step 20 from proof test-div-04 (previous step)

div(mkDecimal(5540535, 4), mkDecimal(45, 4), 0) * mkDecimal(45, 4) = mkDecimal(5540535, 4) ⊦ div(mkDecimal(5540535, 4), mkDecimal(45, 4), 0) = mkDecimal(123123, 0), mkDecimal(5540535, mkDecimal(123123, 0).scale + mkDecimal(45, 4).scale) = mkDecimal(5540535, 4)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)
Proof step 22:
¬(123123 % 10 = 0 ∧ 0 ≠ 0 ∧ 123123 ≠ 0), div(mkDecimal(5540535, 4), mkDecimal(45, 4), 0) * mkDecimal(45, 4) = mkDecimal(5540535, 4) ⊦ div(mkDecimal(5540535, 4), mkDecimal(45, 4), 0) = mkDecimal(123123, 0), mkDecimal(5540535, abs(0) + mkDecimal(45, 4).scale) = mkDecimal(5540535, 4)

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, 123123] flags: rewrite

Additional information

Used terms: 0, 123123