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Proof step 32 from proof BertrandsPostulate (previous step)

0 < i, i ≤ 2 ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i ≠ j → (i ≤ j ↔ i < j)
Proof step 34:
¬ i ≠ 2, 0 < i, i ≤ 2 ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

Rule argument

spec: int-abs inst: name: lels-02 seq: ⊦ i ≠ j → (i ≤ j ↔ i < j) subst: [j, i] → [2, i] flags: rewrite

Additional information

Used simplifier rules: two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%one-01: ⊦ i = 1 → i * j = j; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%prime-le-2: ⊦ prime(i) → (i ≤ 2 ↔ i = 2); from specification int-gcd%prime-two-01: ⊦ prime(2); from specification int-gcd Used terms: 2, i