Nuprl Lemma : ts-refinement-reachable
∀[ts1,ts2:transition-system{i:l}]. ∀[f:ts-type(ts2) ⟶ ts-type(ts1)].
∀[s:ts-reachable(ts2)]. (f s ∈ ts-reachable(ts1)) supposing ts-refinement(ts1;ts2;f)
Proof
Definitions occuring in Statement :
ts-refinement: ts-refinement(ts1;ts2;f),
ts-reachable: ts-reachable(ts),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
ts-reachable: ts-reachable(ts),
member: t ∈ T,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
all: ∀x:A. B[x],
infix_ap: x f y,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
prop: ℙ,
ts-refinement: ts-refinement(ts1;ts2;f),
and: P ∧ Q
Lemmas referenced :
rel_star_transitivity,
ts-type_wf,
ts-rel_wf,
ts-init_wf,
ts-refinement-reachable2,
ts-init_wf_reachable,
rel_star_wf,
ts-reachable_wf,
subtype_rel_wf,
ts-refinement_wf,
transition-system_wf
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
setElimination,
thin,
rename,
cut,
dependent_set_memberEquality,
applyEquality,
hypothesisEquality,
lemma_by_obid,
isectElimination,
hypothesis,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
setEquality,
universeEquality,
cumulativity,
functionEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
productElimination
Latex:
\mforall{}[ts1,ts2:transition-system\{i:l\}]. \mforall{}[f:ts-type(ts2) {}\mrightarrow{} ts-type(ts1)].
\mforall{}[s:ts-reachable(ts2)]. (f s \mmember{} ts-reachable(ts1)) supposing ts-refinement(ts1;ts2;f)
Date html generated:
2016_05_15-PM-05_42_27
Last ObjectModification:
2015_12_27-PM-00_31_10
Theory : general
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