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Proof step 10 from proof test-div-04 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal-simple-ops inst: name: mult-eq-same seq: ⊦ dec ≠ mkDecimal(0, 0) → (dec_i * dec = dec_j * dec ↔ dec_i = dec_j) subst: [dec_j, dec, dec_i] → [mkDecimal(123123, 0), mkDecimal(45, 4), div (mkDecimal(123123, 0) * mkDecimal(45, 4), mkDecimal(45, 4), 0)] flags: rewrite

Additional information

Used simplifier rules: eq-zero: ⊦ mkDecimal(i, j) = mkDecimal(0, j0) ↔ i = 0; from specification decimal Used terms: mkDecimal(123123, 0), mkDecimal(45, 4), div(mkDecimal(123123, 0) * mkDecimal(45, 4), mkDecimal(45, 4), 0)