[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 8 from proof prime-odd-01 (previous step)

prime(i0 + 1) ⊦ i0 % 2 = 0, (i0 + 1) % 2 = 0, 1 = i0

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-div name: div-elim-pospos seq: ⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0) subst: [i, j, i0, j0] → [i0, 2, i, j]

Additional information

Used simplifier rules: ⊦ i ≠ j → (i ≤ j ↔ i < j); (s)% ⊦ 0 < j → (j < 2 ↔ j = 1); (s)%forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (j * i + i0) % j = i0 % j; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i ≤ j ↔ ¬ j < i; (ss)% ⊦ i < 0 → ((i + 1) % 2 = 0 ↔ ¬((i + 1) % 2 = ~1 ∧ i % 2 = 0)); (ss)% ⊦ i < 0 ∧ i % 2 = 0 → (i + 1) % 2 = ~1; (s)%⊦ 0 < j ∧ 0 ≤ i → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ 0 ≤ j0 ∧ j0 < j ∧ 0 ≤ i0); (elim) Used terms: i0, 2, i, j