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Theorem prime-def-mod

⊦ 1 < j → (prime(j) ↔ (∀ i. 1 < i ∧ i * i ≤ j → j % i ≠ 0))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: prime-11, prime-1259, prime-13, prime-163, prime-23, prime-29, prime-317, prime-43, prime-5, prime-631, prime-7, prime-83, prime-not-four, prime-three,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 9
Proof steps: 17
Used lemmas: divides, div-mult, prime-def,
Used spec theorems:
- int-div/modex
Used simplifier rules: