Nuprl Lemma : type-continuous'_wf
∀[F:Type ⟶ Type]. (semi-continuous(λT.F[T]) ∈ ℙ')
Proof
Definitions occuring in Statement :
type-continuous': semi-continuous(λT.F[T]),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
type-continuous': semi-continuous(λT.F[T]),
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
type-incr-chain: type-incr-chain{i:l}()
Lemmas referenced :
uall_wf,
type-incr-chain_wf,
subtype_rel_wf,
tunion_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
lambdaEquality,
cumulativity,
applyEquality,
hypothesisEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. (semi-continuous(\mlambda{}T.F[T]) \mmember{} \mBbbP{}')
Date html generated:
2016_05_15-PM-06_52_30
Last ObjectModification:
2015_12_27-AM-11_43_25
Theory : general
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