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Proof step 5 from proof mod-twoodd-03 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: mod-neg-01 seq: j ≠ 0 ⊦ ~ i % j = ~(i % j) subst: [j, i] → [2 * j, 2 * (~ i - 1) + 1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 2 * i = 0 ↔ i = 0; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ ~ i - j = ~(i + j); (s)% ⊦ ~ i * j = ~(i * j); (s)% ⊦ i + ~ j = i - j; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ ~(i - j) = j - i; (s) Used terms: 2 * j, 2 * (~ i - 1) + 1