[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 12 from proof div-two-intro (previous step)

i < 0 ⊦ i % 2 = 0, i / (j0 * 2) = (i / 2) / j0, j0 = 0

User applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
⊦ 0 < j ∧ i < 0 → (i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0)
Proof step 14:
i = i0 * 2 + j1, i < 0, abs(j1) < 2, 0 < 2, j1 ≤ 0, i0 ≤ 0 ⊦ i / (j0 * 2) = i0 / j0, j0 = 0, j1 = 0

Rule argument

spec: <toplevel> name: div-elim-negpos seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [i, 2, i0, j] flags: <rotated> <all paths>

Additional information

Used simplifier rules: ⊦ i < 0 ∧ 0 ≤ j → i < j; (s) Used terms: i, 2, i0, j