Nuprl Lemma : ts-reachable_wf
∀[ts:transition-system{i:l}]. (ts-reachable(ts) ∈ {T:Type| T ⊆r ts-type(ts)} )
Proof
Definitions occuring in Statement :
ts-reachable: ts-reachable(ts),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
set: {x:A| B[x]} ,
universe: Type
Definitions unfolded in proof :
ts-reachable: ts-reachable(ts),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
ts-init: ts-init(ts),
ts-rel: ts-rel(ts),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
subtype_rel_wf,
pi1_wf_top,
rel_star_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
setElimination,
thin,
rename,
hypothesisEquality,
setEquality,
because_Cache,
dependent_set_memberEquality,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
instantiate,
universeEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
productEquality,
cumulativity,
functionEquality
Latex:
\mforall{}[ts:transition-system\{i:l\}]. (ts-reachable(ts) \mmember{} \{T:Type| T \msubseteq{}r ts-type(ts)\} )
Date html generated:
2016_05_15-PM-05_39_22
Last ObjectModification:
2015_12_27-PM-02_05_57
Theory : general
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