Nuprl Lemma : Rtrans_wf
∀K:dl_KS. ∀r,s,t:worlds(K). (Rtrans(K;r;s;t) ∈ rRs ⇒ sRt ⇒ rRt)
Proof
Definitions occuring in Statement :
Rtrans: Rtrans(k;r;s;t),
dl_KS: dl_KS,
KrRel: sRt,
worlds: worlds(k),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
Rtrans: Rtrans(k;r;s;t),
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,
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,
inhabitedIsType,
universeIsType
Latex:
\mforall{}K:dl\_KS. \mforall{}r,s,t:worlds(K). (Rtrans(K;r;s;t) \mmember{} rRs {}\mRightarrow{} sRt {}\mRightarrow{} rRt)
Date html generated:
2020_05_20-AM-09_01_36
Last ObjectModification:
2019_11_27-PM-02_24_27
Theory : dynamic!logic
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