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Proof step 12 from proof test-div-04 (previous step)

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

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

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(45, 4), mkDecimal(123123, 0)] flags: rewrite

Additional information

Used terms: mkDecimal(45, 4), mkDecimal(123123, 0)