Nuprl Lemma : coSet-subtype-Set
∀B:Set{i:l}. ({u:coSet{i:l}| (u ∈ B)} ⊆r Set{i:l})
Proof
Definitions occuring in Statement :
Set: Set{i:l},
setmem: (x ∈ s),
coSet: coSet{i:l},
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
set: {x:A| B[x]}
Definitions unfolded in proof :
prop: ℙ,
exists: ∃x:A. B[x],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x]
Lemmas referenced :
Set_wf,
set-subtype-coSet,
coSet_wf,
setmem_wf,
coSet-mem-Set-implies-Set
Rules used in proof :
cumulativity,
setEquality,
sqequalRule,
because_Cache,
applyEquality,
hypothesis,
dependent_pairFormation,
independent_isectElimination,
hypothesisEquality,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
rename,
thin,
setElimination,
lambdaEquality,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}B:Set\{i:l\}. (\{u:coSet\{i:l\}| (u \mmember{} B)\} \msubseteq{}r Set\{i:l\})
Date html generated:
2018_07_29-AM-09_51_45
Last ObjectModification:
2018_07_20-PM-01_03_15
Theory : constructive!set!theory
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