Nuprl Lemma : not-atom-member-int
∀[t:Atom]. (¬(t ∈ ℤ))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
int: ℤ,
atom: Atom
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
prop: ℙ
Lemmas referenced :
isatom-implies-not-isint,
atom_subtype_base,
value-type-has-value,
int-value-type,
equal-wf-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
applyEquality,
hypothesis,
sqequalRule,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
isintReduceTrue,
independent_functionElimination,
natural_numberEquality,
voidElimination,
intEquality,
lambdaEquality,
dependent_functionElimination,
atomEquality,
isatomReduceTrue
Latex:
\mforall{}[t:Atom]. (\mneg{}(t \mmember{} \mBbbZ{}))
Date html generated:
2016_05_13-PM-03_28_06
Last ObjectModification:
2015_12_26-AM-09_27_28
Theory : call!by!value_1
Home
Index