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Proof step 12 from proof div-twoodd-07 (previous step)

j * 2 < 0, j < 0, i < 0 ⊦ ~((2 * (i + 1) - 1) / (2 * ~ j)) = (i + 1) / j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
i < 0, 0 < j ⊦ (2 * i - 1) / (2 * j) = i / j
Proof step 14:
i < 0, j < 0, j * 2 < 0 ⊦ ~((2 * (i + 1) - 1) / (2 * ~ j)) = (i + 1) / j, i + 1 < 0 ∧ 0 < ~ j

Rule argument

spec: <toplevel> name: div-twoodd-03 seq: i < 0, 0 < j ⊦ (2 * i - 1) / (2 * j) = i / j subst: [j, i] → [~ j, i + 1] flags: <all paths>

Additional information

Used simplifier rules: neg: j ≠ 0 ⊦ i / ~ j = ~(i / j);% ⊦ ~ ~ i = i; (s) Used terms: ~ j, i + 1