Nuprl Lemma : ts-init_wf_reachable
∀[ts:transition-system{i:l}]. (ts-init(ts) ∈ ts-reachable(ts))
Proof
Definitions occuring in Statement :
ts-reachable: ts-reachable(ts),
ts-init: ts-init(ts),
transition-system: transition-system{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
ts-reachable: ts-reachable(ts),
infix_ap: x f y,
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
rel_star_weakening,
ts-type_wf,
ts-init_wf,
ts-rel_wf,
rel_star_wf,
transition-system_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
independent_isectElimination,
dependent_set_memberEquality,
applyEquality,
lambdaEquality,
sqequalRule,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[ts:transition-system\{i:l\}]. (ts-init(ts) \mmember{} ts-reachable(ts))
Date html generated:
2016_05_15-PM-05_41_10
Last ObjectModification:
2015_12_27-PM-00_32_00
Theory : general
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