Nuprl Lemma : emptyset-transitive
transitive-set({})
Proof
Definitions occuring in Statement :
transitive-set: transitive-set(s),
emptyset: {}
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
prop: ℙ,
false: False,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
setsubset_wf,
all_wf,
setmem_wf,
setmem-emptyset,
coSet_wf,
false_wf,
set-subtype-coSet,
emptyset_wf,
transitive-set-iff
Rules used in proof :
because_Cache,
functionEquality,
lambdaEquality,
instantiate,
isectElimination,
cumulativity,
hypothesisEquality,
impliesFunctionality,
allFunctionality,
addLevel,
voidElimination,
lambdaFormation,
independent_functionElimination,
productElimination,
sqequalRule,
applyEquality,
hypothesis,
thin,
dependent_functionElimination,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut
Latex:
transitive-set(\{\})
Date html generated:
2018_07_29-AM-10_02_56
Last ObjectModification:
2018_07_18-PM-01_35_18
Theory : constructive!set!theory
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