Nuprl Lemma : connected_wf
∀[X:Type]. Connected(X) ∈ ℙ' supposing X ⊆r ℝ
Proof
Definitions occuring in Statement :
connected: Connected(X),
real: ℝ,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
connected: Connected(X),
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
so_apply: x[s],
and: P ∧ Q
Lemmas referenced :
uall_wf,
real_wf,
all_wf,
req_wf,
exists_wf,
or_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
functionEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
hypothesisEquality,
universeEquality,
setEquality,
because_Cache,
lambdaFormation,
setElimination,
rename,
functionExtensionality,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[X:Type]. Connected(X) \mmember{} \mBbbP{}' supposing X \msubseteq{}r \mBbbR{}
Date html generated:
2017_10_03-AM-10_11_23
Last ObjectModification:
2017_07_10-AM-10_42_58
Theory : reals
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