Nuprl Lemma : positive-prime-divides-prime
∀[p,q:ℕ]. (p = q ∈ ℕ) supposing ((p | q) and prime(q) and prime(p))
Proof
Definitions occuring in Statement :
prime: prime(a),
divides: b | a,
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
nat: ℕ,
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
le_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
itermConstant_wf,
intformle_wf,
decidable__le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_properties,
assoced_nelim,
prime_wf,
divides_wf,
prime-divides-prime
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
independent_functionElimination,
isectElimination,
sqequalRule,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
productElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
dependent_set_memberEquality
Latex:
\mforall{}[p,q:\mBbbN{}]. (p = q) supposing ((p | q) and prime(q) and prime(p))
Date html generated:
2016_05_14-PM-04_27_12
Last ObjectModification:
2016_01_14-PM-11_35_02
Theory : num_thy_1
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