Nuprl Lemma : bounded-ccc-nset-finite
∀K:Type. (CCCNSet(K) ⇒ (∀B:ℕ. ((∀k:K. (k ≤ B)) ⇒ finite(K))))
Proof
Definitions occuring in Statement :
ccc-nset: CCCNSet(K),
finite: finite(T),
nat: ℕ,
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
nat: ℕ,
guard: {T},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
and: P ∧ Q,
ccc-nset: CCCNSet(K),
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
istype-universe,
ccc-nset_wf,
istype-nat,
nat_wf,
subtype_rel_transitivity,
istype-le,
bounded-decidable-nset-finite,
bounded-ccc-nset-decidable
Rules used in proof :
universeEquality,
instantiate,
independent_isectElimination,
intEquality,
Error :inhabitedIsType,
rename,
setElimination,
Error :lambdaEquality_alt,
applyEquality,
isectElimination,
Error :universeIsType,
Error :functionIsType,
sqequalRule,
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{} (\mforall{}B:\mBbbN{}. ((\mforall{}k:K. (k \mleq{} B)) {}\mRightarrow{} finite(K))))
Date html generated:
2019_06_20-PM-03_02_40
Last ObjectModification:
2019_06_13-PM-04_17_15
Theory : continuity
Home
Index