Nuprl Lemma : aFPersistent
∀K:dl_KS. ∀i:worlds(K). ∀a:ℕ. (atmFrc_prop(K;a;i) ⇒ (∀j:worlds(K). (iRj ⇒ atmFrc_prop(K;a;j))))
Proof
Definitions occuring in Statement :
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
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
guard: {T}
Lemmas referenced :
atmFrcPersistent_wf,
KrRel_wf,
dl_KS_subtype,
atmFrc_prop_wf,
istype-nat,
worlds_wf,
dl_KS_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
independent_functionElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
universeIsType,
isectElimination,
applyEquality,
sqequalRule,
because_Cache
Latex:
\mforall{}K:dl\_KS. \mforall{}i:worlds(K). \mforall{}a:\mBbbN{}. (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_42
Last ObjectModification:
2019_11_27-PM-02_12_48
Theory : dynamic!logic
Home
Index