Nuprl Lemma : plus-set-transitive
∀a:coSet{i:l}. (transitive-set(a) ⇒ transitive-set((a)+))
Proof
Definitions occuring in Statement :
transitive-set: transitive-set(s),
plus-set: (a)+,
coSet: coSet{i:l},
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
seteq_wf,
setmem_functionality,
seteq_weakening,
seteq_inversion,
setmem_wf,
coSet_wf,
setsubset-iff,
setmem-plus-set,
plus-set_wf,
setsubset_wf,
transitive-set-iff,
transitive-set_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
sqequalHypSubstitution,
unionElimination,
thin,
inlFormation_alt,
universeIsType,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
independent_functionElimination,
productElimination,
inhabitedIsType,
sqequalRule,
unionIsType,
functionIsType
Latex:
\mforall{}a:coSet\{i:l\}. (transitive-set(a) {}\mRightarrow{} transitive-set((a)+))
Date html generated:
2020_05_20-PM-01_18_46
Last ObjectModification:
2020_01_06-PM-01_24_15
Theory : constructive!set!theory
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