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Proof step 7 from proof prime-odd-01 (previous step)

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

User applied rule insert elim lemma

And closed the goal!

Rule argument

spec: int-div inst: 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] flags: []

Additional information

Used simplifier rules: lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1%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%numadd-01: ⊦ (* j) = i0 + (* j0) ↔ j - j0 = i0; from specification int-abs%zero-neq-01: ⊦ 0 < i → (i * j = 0 ↔ j = 0); from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%mod-mult-pos-02: ⊦ 0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 → (i * j + i0) % j = i0 % j; from specification int-div%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%modeven-neg-01: ⊦ i < 0 → ((i + 1) % 2 ≠ 0 ↔ (i + 1) % 2 = ~1 ∧ i % 2 = 0); from specification int-div%modeven-neg: ⊦ i < 0 ∧ i % 2 = 0 → (i + 1) % 2 = ~1; from specification int-div%⊦ 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