### 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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