Nuprl Lemma : unordered-combination_wf
∀[T:Type]. ∀[n:ℕ]. (UnorderedCombination(n;T) ∈ Type)
Proof
Definitions occuring in Statement :
unordered-combination: UnorderedCombination(n;T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
unordered-combination: UnorderedCombination(n;T),
subtype_rel: A ⊆r B,
nat: ℕ,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
bag_wf,
and_wf,
bag-no-repeats_wf,
equal_wf,
bag-size_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. (UnorderedCombination(n;T) \mmember{} Type)
Date html generated:
2016_05_15-PM-03_11_38
Last ObjectModification:
2015_12_27-AM-09_24_10
Theory : bags
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