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Proof step 6 from proof nummult-ls-02 (previous step)

j0 < i, 0 < i, i0 ≤ i1, i1 * i + j0 < i * i0, 0 < i0, 0 ≤ j0, 0 ≤ i1, 0 < i1 ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: numls-02 seq: ⊦ (* i2) * i + j < (* i1) * i ↔ j < (i1 - i2) * i subst: [i1, j, i, i2] → [i0, j0, i, i1] flags: rewrite

Additional information

Used simplifier rules: forward-lels: ⊦ i ≤ j ∧ j < j0 → i < j0; (forward) from specification int-abs%zero-gr: ⊦ 0 < i → (0 < i * j ↔ 0 < j); from specification int-mult%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%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: i0, j0, i, i1