Nuprl Lemma : ts-refinement-reachable2
∀ts1,ts2:transition-system{i:l}. ∀f:ts-type(ts2) ⟶ ts-type(ts1).
(ts-refinement(ts1;ts2;f)
⇒ (∀s1,s2:ts-reachable(ts2). ((s1 (ts-rel(ts2)^*) s2) ⇒ ((f s1) (ts-rel(ts1)^*) (f s2)))))
Proof
Definitions occuring in Statement :
ts-refinement: ts-refinement(ts1;ts2;f),
ts-reachable: ts-reachable(ts),
ts-rel: ts-rel(ts),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
rel_star: R^*,
infix_ap: x f y,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
ts-reachable: ts-reachable(ts),
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
infix_ap: x f y,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
guard: {T},
ts-refinement: ts-refinement(ts1;ts2;f),
and: P ∧ Q
Lemmas referenced :
rel-preserving-star-reachable,
ts-type_wf,
ts-init_wf,
ts-rel_wf,
set_wf,
rel_star_wf,
ts-refinement_wf,
transition-system_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
setElimination,
rename,
sqequalRule,
lambdaEquality,
universeEquality,
because_Cache,
functionEquality,
productElimination
Latex:
\mforall{}ts1,ts2:transition-system\{i:l\}. \mforall{}f:ts-type(ts2) {}\mrightarrow{} ts-type(ts1).
(ts-refinement(ts1;ts2;f)
{}\mRightarrow{} (\mforall{}s1,s2:ts-reachable(ts2).
((s1 rel\_star(ts-type(ts2); ts-rel(ts2)) s2) {}\mRightarrow{} ((f s1) (ts-rel(ts1)\^{}*) (f s2)))))
Date html generated:
2016_05_15-PM-05_42_16
Last ObjectModification:
2015_12_27-PM-00_31_29
Theory : general
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