Nuprl Lemma : ts-stable-rel_wf
∀[ts:transition-system{i:l}]. ∀[R:ts-type(ts) ⟶ ts-type(ts) ⟶ ℙ]. (ts-stable-rel(ts;x,y.R[x;y]) ∈ ℙ)
Proof
Definitions occuring in Statement :
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y]),
ts-type: ts-type(ts),
transition-system: transition-system{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ts-stable-rel: ts-stable-rel(ts;x,y.R[x; y]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
infix_ap: x f y,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf,
ts-type_wf,
rel_star_wf,
ts-rel_wf,
transition-system_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[ts:transition-system\{i:l\}]. \mforall{}[R:ts-type(ts) {}\mrightarrow{} ts-type(ts) {}\mrightarrow{} \mBbbP{}].
(ts-stable-rel(ts;x,y.R[x;y]) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-05_43_18
Last ObjectModification:
2015_12_27-PM-00_30_33
Theory : general
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