Nuprl Lemma : weak-overt-implies-overt
∀[X:Type]. (wOvert(X) ⇒ Overt(X))
Proof
Definitions occuring in Statement :
weak-overt: wOvert(X),
overt: Overt(X),
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
weak-overt: wOvert(X),
overt: Overt(X),
member: t ∈ T,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
sp-le: x ≤ y,
Open: Open(X),
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
rev_implies: P ⇐ Q,
in-open: x ∈ A,
not: ¬A,
false: False
Lemmas referenced :
equal-wf-T-base,
Sierpinski_wf,
all_wf,
sp-le_wf,
Open_wf,
iff_wf,
weak-overt_wf,
not_wf,
exists_wf,
not-Sierpinski-bottom,
Sierpinski-unequal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
cut,
hypothesis,
isectElimination,
thin,
hypothesisEquality,
productElimination,
dependent_pairFormation,
introduction,
sqequalRule,
independent_pairEquality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
extract_by_obid,
applyEquality,
baseClosed,
because_Cache,
cumulativity,
functionExtensionality,
productEquality,
universeEquality,
independent_pairFormation,
functionEquality,
independent_functionElimination,
voidElimination,
equalitySymmetry,
equalityTransitivity
Latex:
\mforall{}[X:Type]. (wOvert(X) {}\mRightarrow{} Overt(X))
Date html generated:
2019_10_31-AM-07_19_17
Last ObjectModification:
2017_07_28-AM-09_12_25
Theory : synthetic!topology
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