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Proof step 27 from proof div-nearer-zero (previous step)

j < 0, j * i / j < i, i < 0, ~ i < ~ j * ~ i / ~ j ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: ls-same-pos-02 seq: ⊦ 0 ≤ i ∧ 0 < j → ¬ i < i / j * j subst: [j, i] → [~ j, ~ i] flags: <all paths>

Additional information

Used simplifier rules: neg-01: j ≠ 0 ⊦ ~ i / j = ~(i / j);%Div-right: ⊦ j ≠ 0 → i / ~ j = ~(i / j);% ⊦ ~ i = 0 ↔ i = 0; (s)% ⊦ ~ ~ i = i; (s)% ⊦ ~ i * j = ~(i * j); (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ ~ j < ~ i ↔ i < j; (s)% ⊦ i ≤ ~ j ↔ i + j ≤ 0; (s)% ⊦ i + 0 = i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < ~ i ↔ i < 0; (s)% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < j → ¬ j < i; (s)%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: ~ j, ~ i