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Proof step 29 from proof test-div-03 (previous step)

div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) * mkDecimal(1000, 0) = mkDecimal(1, 0) ⊦ div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) = mkDecimal(1, 3), mkDecimal(100, 2) = mkDecimal(1, 0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1)
Proof step 31:
100 % 10 = 0 ∧ 2 ≠ 0, div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) * mkDecimal(1000, 0) = mkDecimal(1, 0) ⊦ div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) = mkDecimal(1, 3), mkDecimal(100 / 10, abs(2) - 1) = mkDecimal(1, 0)

Rule argument

spec: decimal inst: name: mkDecimal-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1) subst: [j, i] → [2, 100] flags: rewrite

Additional information

Used terms: 2, 100