Nuprl Lemma : transmem_transitivity
Trans(coSet{i:l};x,y.(x ∈∈ y))
Proof
Definitions occuring in Statement :
transmem: (x ∈∈ y),
coSet: coSet{i:l},
trans: Trans(T;x,y.E[x; y])
Definitions unfolded in proof :
all: ∀x:A. B[x],
trans: Trans(T;x,y.E[x; y]),
utrans: UniformlyTrans(T;x,y.E[x; y]),
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
transmem: (x ∈∈ y)
Lemmas referenced :
setmem_wf,
coSet_wf,
transitive-closure-transitive
Rules used in proof :
because_Cache,
lambdaFormation,
hypothesisEquality,
cumulativity,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
instantiate,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
Trans(coSet\{i:l\};x,y.(x \mmember{}\mmember{} y))
Date html generated:
2018_07_29-AM-10_03_27
Last ObjectModification:
2018_07_18-PM-11_37_36
Theory : constructive!set!theory
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