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Proof step 4 from proof square-int-nlz (previous step)

(mkDecimal(i, i0) * mkDecimal(i, i0)).int < 0 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: inst: name: mult-def-any seq: ⊦ mkDecimal(i, j) * mkDecimal(i0, j0) = mkDecimal(i * i0, abs(j) + abs(j0)) subst: [j0, i0, j, i] → [i0, i, i0, i] flags: rewrite, current

Additional information

Used simplifier rules: add-mult-two: ⊦ i + i = 2 * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%getint-neg-02: ⊦ mkDecimal(i, j).int < 0 ↔ i < 0; from specification decimal%square-lez: ⊦ ¬ i * i < 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, i, i0, i