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Proof step 2 from proof bertrand-holds-lower (previous step)

i ≤ 1024, 0 < i ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

User applied rule insert lemma

And obtained the following new goals

Proof step 3:
⊦ prime(2) ∧ prime(3) ∧ prime(5) ∧ prime(7) ∧ prime(13) ∧ prime(23) ∧ prime(43) ∧ prime(83) ∧ prime(163) ∧ prime(317) ∧ prime(631) ∧ prime(1259)
Proof step 4:
prime(2) ∧ prime(3) ∧ prime(5) ∧ prime(7) ∧ prime(13) ∧ prime(23) ∧ prime(43) ∧ prime(83) ∧ prime(163) ∧ prime(317) ∧ prime(631) ∧ prime(1259), i ≤ 1024, 0 < i ⊦ ∃ j. prime(j) ∧ i < j ∧ j ≤ 2 * i

Rule argument

spec: inst: name: small-primes seq: ⊦ prime(2) ∧ prime(3) ∧ prime(5) ∧ prime(7) ∧ prime(13) ∧ prime(23) ∧ prime(43) ∧ prime(83) ∧ prime(163) ∧ prime(317) ∧ prime(631) ∧ prime(1259) subst: flags: current, []

Additional information

Used terms: