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Proof step 6 from proof mult-pos-02 (previous step)

mkDecimal(i, i0) * mkDecimal(i1, i2) < mkDecimal(i, i0), mkDecimal(i, i0) * mkDecimal(i1, i2) < mkDecimal(0, 0), mkDecimal(i, i0) * mkDecimal(i1, i2) < mkDecimal(i1, i2), 0 ≤ i, 0 ≤ i1 ⊦

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] → [i2, i1, i0, i] flags: rewrite, current

Additional information

Used simplifier rules: ls-zero-01: ⊦ mkDecimal(i, i0) < mkDecimal(0, 0) ↔ i < 0;%zero-ls-02: ⊦ 0 ≤ i → (i * j < 0 ↔ ¬ ¬(j < 0 ∧ i ≠ 0)); from specification int-mult%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i2, i1, i0, i