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Proof step 12 from proof test-div-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ dec_i * dec_j = mkDecimal(dec_i.int * dec_j.int, dec_i.scale + dec_j.scale)
Proof step 14:
div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) * mkDecimal(1000, 0) = mkDecimal(1, 0) ⊦ mkDecimal(mkDecimal(1, 3).int * mkDecimal(1000, 0).int, mkDecimal(1, 3).scale + mkDecimal(1000, 0).scale) = mkDecimal(1, 0), div(mkDecimal(1, 0), mkDecimal(1000, 0), 0) = mkDecimal(1, 3)

Rule argument

spec: decimal-simple-ops 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(1000, 0), mkDecimal(1, 3)] flags: rewrite

Additional information

Used terms: mkDecimal(1000, 0), mkDecimal(1, 3)