Nuprl Lemma : bar-type-continuous
∀[X:ℕ ⟶ {T:Type| value-type(T)} ]. ((⋂n:ℕ. bar(X[n])) ⊆r bar(⋂n:ℕ. X[n]))
Proof
Definitions occuring in Statement :
bar: bar(T),
nat: ℕ,
value-type: value-type(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
set: {x:A| B[x]} ,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
bar: bar(T)
Lemmas referenced :
partial-type-continuous
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
hypothesis
Latex:
\mforall{}[X:\mBbbN{} {}\mrightarrow{} \{T:Type| value-type(T)\} ]. ((\mcap{}n:\mBbbN{}. bar(X[n])) \msubseteq{}r bar(\mcap{}n:\mBbbN{}. X[n]))
Date html generated:
2016_05_15-PM-10_04_36
Last ObjectModification:
2016_01_05-PM-06_42_12
Theory : bar!type
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