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Proof step 25 from proof bertrand-holds-lower (previous step)

prime(5), prime(7), prime(13), prime(23), prime(43), prime(83), prime(163), prime(317), prime(631), prime(1259), i ≤ 1024, 0 < i, i < 3 ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: 3 abort: F discard: F computed: F

Additional information

Used simplifier rules: prime-three: ⊦ prime(3); from specification int-gcd%numlelsdel: j0 ≠ 0, j ≤ j0 ⊦ i < (* j) → i < (* j0); from specification int-abs%nummult-le-02: ⊦ 0 < i ∧ 0 ≤ j → ((* j) ≤ (* i) * i0 ↔ (i + j - 1) / i ≤ i0); from specification int-div%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%two-ls: ⊦ 0 < j → (j < 2 ↔ j = 1); from specification int-basic1%one-01: ⊦ i = 1 → i * j = j; 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: 3