Nuprl Lemma : cardinality-le-finite
∀[T:Type]. ∀n:ℕ. (|T| ≤ n ⇒ finite-type(T))
Proof
Definitions occuring in Statement :
cardinality-le: |T| ≤ n,
finite-type: finite-type(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
finite-type: finite-type(T),
cardinality-le: |T| ≤ n,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
exists_wf,
int_seg_wf,
surject_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
hypothesisEquality,
hypothesis,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
setElimination,
rename,
lambdaEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}n:\mBbbN{}. (|T| \mleq{} n {}\mRightarrow{} finite-type(T))
Date html generated:
2016_05_14-PM-01_51_40
Last ObjectModification:
2015_12_26-PM-05_37_42
Theory : list_1
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