Nuprl Lemma : set-add_wf
∀[a,b:coSet{i:l}]. (a + b ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
set-add: a + b,
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
set-add: a + b,
mk-coset: mk-coset(T;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
subtype_coSet,
coSet_subtype,
mk-coset_wf,
equal_wf,
coSet_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis_subsumption,
extract_by_obid,
hypothesis,
hypothesisEquality,
applyEquality,
sqequalHypSubstitution,
sqequalRule,
productElimination,
thin,
isectElimination,
unionEquality,
lambdaEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
unionElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[a,b:coSet\{i:l\}]. (a + b \mmember{} coSet\{i:l\})
Date html generated:
2019_10_31-AM-06_33_20
Last ObjectModification:
2018_08_21-PM-02_01_17
Theory : constructive!set!theory
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