Nuprl Lemma : ccc-nset-not-not-finite
∀K:Type. (CCCNSet(K) ⇒ (¬¬finite(K)))
Proof
Definitions occuring in Statement :
ccc-nset: CCCNSet(K),
finite: finite(T),
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
ccc-nset: CCCNSet(K),
prop: ℙ,
uall: ∀[x:A]. B[x],
false: False,
or: P ∨ Q,
not: ¬A,
and: P ∧ Q,
transparent-nset: Transparent(K),
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
unbounded-decidable-nset-infinite,
not-CCC-infinite,
istype-universe,
ccc-nset_wf,
istype-void,
finite_wf,
unbounded-ccc-nset-decidable,
istype-nat,
bounded-ccc-nset-finite,
ccc-nset-transparent
Rules used in proof :
universeEquality,
instantiate,
isectElimination,
Error :universeIsType,
Error :functionIsType,
sqequalRule,
voidElimination,
because_Cache,
unionElimination,
productElimination,
independent_functionElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}K:Type. (CCCNSet(K) {}\mRightarrow{} (\mneg{}\mneg{}finite(K)))
Date html generated:
2019_06_20-PM-03_02_44
Last ObjectModification:
2019_06_13-PM-07_18_49
Theory : continuity
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