Nuprl Lemma : not-pair-member-int
∀[a,b:Base]. (¬(<a, b> ∈ ℤ))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
not: ¬A,
member: t ∈ T,
pair: <a, b>,
int: ℤ,
base: Base
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
uimplies: b supposing a,
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True,
false: False,
all: ∀x:A. B[x]
Lemmas referenced :
base_wf,
ispair-implies-not-isint,
value-type-has-value,
int-value-type
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
Error :inhabitedIsType,
hypothesisEquality,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
hypothesis,
Error :lambdaFormation_alt,
sqequalRule,
Error :equalityIsType4,
intEquality,
baseApply,
closedConclusion,
baseClosed,
because_Cache,
sqequalHypSubstitution,
isectElimination,
thin,
independent_isectElimination,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
independent_functionElimination,
isintReduceTrue,
Error :equalityIsType1,
dependent_functionElimination,
voidElimination
Latex:
\mforall{}[a,b:Base]. (\mneg{}(<a, b> \mmember{} \mBbbZ{}))
Date html generated:
2019_06_20-AM-11_21_38
Last ObjectModification:
2018_09_27-PM-07_01_32
Theory : call!by!value_1
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