Nuprl Lemma : prime-divides-prime
∀p,q:ℤ. (prime(p) ⇒ prime(q) ⇒ (p | q) ⇒ (p ~ q))
Proof
Definitions occuring in Statement :
prime: prime(a),
assoced: a ~ b,
divides: b | a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
prime: prime(a),
and: P ∧ Q,
member: t ∈ T,
or: P ∨ Q,
not: ¬A,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
divides-prime,
divides_wf,
prime_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
lemma_by_obid,
dependent_functionElimination,
hypothesisEquality,
independent_functionElimination,
hypothesis,
unionElimination,
voidElimination,
isectElimination,
intEquality
Latex:
\mforall{}p,q:\mBbbZ{}. (prime(p) {}\mRightarrow{} prime(q) {}\mRightarrow{} (p | q) {}\mRightarrow{} (p \msim{} q))
Date html generated:
2016_05_14-PM-04_27_08
Last ObjectModification:
2015_12_26-PM-08_05_29
Theory : num_thy_1
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