Nuprl Lemma : ts-refinement_wf
∀[ts1,ts2:transition-system{i:l}]. ∀[f:ts-type(ts2) ⟶ ts-type(ts1)]. (ts-refinement(ts1;ts2;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
ts-refinement: ts-refinement(ts1;ts2;f),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ts-refinement: ts-refinement(ts1;ts2;f),
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
so_apply: x[s],
uimplies: b supposing a,
ts-reachable: ts-reachable(ts),
all: ∀x:A. B[x],
infix_ap: x f y,
exists: ∃x:A. B[x]
Lemmas referenced :
infix_ap_wf,
ts-type_wf,
rel_star_wf,
ts-rel_wf,
ts-init_wf,
all_wf,
ts-reachable_wf,
subtype_rel_set,
subtype_rel_wf,
subtype_rel_dep_function,
ts-final_wf,
exists_wf,
equal_wf,
transition-system_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
cumulativity,
universeEquality,
because_Cache,
functionExtensionality,
functionEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[ts1,ts2:transition-system\{i:l\}]. \mforall{}[f:ts-type(ts2) {}\mrightarrow{} ts-type(ts1)].
(ts-refinement(ts1;ts2;f) \mmember{} \mBbbP{})
Date html generated:
2018_05_21-PM-08_00_34
Last ObjectModification:
2017_07_26-PM-05_37_25
Theory : general
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