Nuprl Lemma : cardinality-le_wf
∀[T:Type]. ∀[n:ℕ]. (|T| ≤ n ∈ ℙ)
Proof
Definitions occuring in Statement :
cardinality-le: |T| ≤ n,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
cardinality-le: |T| ≤ n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. (|T| \mleq{} n \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-01_51_33
Last ObjectModification:
2015_12_26-PM-05_37_09
Theory : list_1
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