Nuprl Lemma : not-axiom-member-int
¬(Ax ∈ ℤ)
Proof
Definitions occuring in Statement :
not: ¬A,
member: t ∈ T,
int: ℤ,
axiom: Ax
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
all: ∀x:A. B[x],
false: False
Lemmas referenced :
equal-wf-base,
isaxiom-implies-not-isint,
value-type-has-value,
int-value-type,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
baseClosed,
because_Cache,
hypothesis,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_functionElimination,
isintReduceTrue,
hypothesisEquality,
dependent_functionElimination,
voidElimination
Latex:
\mneg{}(Ax \mmember{} \mBbbZ{})
Date html generated:
2017_04_14-AM-07_15_51
Last ObjectModification:
2017_02_27-PM-02_50_58
Theory : call!by!value_1
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