Nuprl Lemma : atmFrcPersistent_wf
∀K:dl_KS. ∀i:worlds(K). ∀a:ℕ.
(atmFrcPersistent(K;i;a) ∈ atmFrc_prop(K;a;i) ⇒ (∀j:worlds(K). (iRj ⇒ atmFrc_prop(K;a;j))))
Proof
Definitions occuring in Statement :
atmFrcPersistent: atmFrcPersistent(k;i;a),
dl_KS: dl_KS,
atmFrc_prop: atmFrc_prop(k;a;s),
KrRel: sRt,
worlds: worlds(k),
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
atmFrcPersistent: atmFrcPersistent(k;i;a),
dl_KS: dl_KS,
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Lemmas referenced :
subtype_rel_self,
worlds_wf,
KrRel_wf,
nat_wf,
atmFrc_prop_wf,
istype-nat,
dl_KS_subtype,
dl_KS_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
sqequalHypSubstitution,
dependentIntersectionElimination,
dependentIntersectionEqElimination,
thin,
hypothesis,
applyEquality,
tokenEquality,
introduction,
extract_by_obid,
isectElimination,
functionEquality,
hypothesisEquality,
functionExtensionality,
universeIsType
Latex:
\mforall{}K:dl\_KS. \mforall{}i:worlds(K). \mforall{}a:\mBbbN{}.
(atmFrcPersistent(K;i;a) \mmember{} atmFrc\_prop(K;a;i) {}\mRightarrow{} (\mforall{}j:worlds(K). (iRj {}\mRightarrow{} atmFrc\_prop(K;a;j))))
Date html generated:
2020_05_20-AM-09_01_39
Last ObjectModification:
2019_11_27-PM-02_10_30
Theory : dynamic!logic
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