Nuprl Lemma : weak-continuity_wf
∀[T,V:Type]. (weak-continuity(T;V) ∈ ℙ)
Proof
Definitions occuring in Statement :
weak-continuity: weak-continuity(T;V),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
weak-continuity: weak-continuity(T;V),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
squash_wf,
exists_wf,
int_seg_wf,
equal_wf,
int_seg_subtype_nat,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
cumulativity,
hypothesisEquality,
lambdaEquality,
because_Cache,
natural_numberEquality,
setElimination,
rename,
applyEquality,
functionExtensionality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality
Latex:
\mforall{}[T,V:Type]. (weak-continuity(T;V) \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_29_10
Last ObjectModification:
2017_07_26-PM-04_23_50
Theory : basic
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