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Proof step 47 from proof mult-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(0 * 10) + i→n(i0) → true → mkDecimal(i1, j) * mkDecimal(i2, j0) = mkDecimal(i1 * i2, abs(j) + abs(j0)) ⊦ j = 0, abs(j) + abs(j0) = 0, mkDecimal(0, abs(j) - 1) * mkDecimal(i0, j0) = mkDecimal(0, abs(j) + abs(j0) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ dec_i * dec_j = mkDecimal(dec_i.int * dec_j.int, dec_i.scale + dec_j.scale)
Proof step 49:
∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(0 * 10) + i→n(i0) → true → mkDecimal(i1, j) * mkDecimal(i2, j0) = mkDecimal(i1 * i2, abs(j) + abs(j0)) ⊦ j = 0, abs(j) + abs(j0) = 0, mkDecimal(mkDecimal(0, abs(j) - 1).int * mkDecimal(i0, j0).int, mkDecimal(0, abs(j) - 1).scale + mkDecimal(i0, j0).scale) = mkDecimal(0, abs(j) + abs(j0) - 1)

Rule argument

spec: inst: name: mult-def seq: ⊦ dec_i * dec_j = mkDecimal(dec_i.int * dec_j.int, dec_i.scale + dec_j.scale) subst: [dec_j, dec_i] → [mkDecimal(i0, j0), mkDecimal(0, abs(j) - 1)] flags: rewrite, current

Additional information

Used terms: mkDecimal(i0, j0), mkDecimal(0, abs(j) - 1)