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Theorem product-negative

∀ i. i ∈ ints → 0 ≤ i ⊦ ¬ Π ints < 0

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: primes-product-not-neg, product-min-not-ls-zero,
Used by units in proved state: int-fac,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 8
Used lemmas: product-one, product-app, prod-empty,
Used spec theorems:
- int-mult/zero-ls
Used simplifier rules:
- list/intlista/in-17
- list/intlista/in-append
- list/intlista/a
- list/intlista/c
- oelem/intlista/ls-le
- int-mult/commutativity
- int-mult/associativity
- int-mult/zero-ls-03
- int-abs/lels
- int-abs/lels-02
- int-basic1/ls-01
- int-abs/forward-le-05
- int-abs/forward-le-02
- oelem/intlista/transitivity
- int-abs/lels-01
- int-abs/zero-gels-01
- int-abs/lels-03