Nuprl Lemma : dl-R_trans
∀K:dl_KS. ∀i,j,k:worlds(K). (iRj ⇒ jRk ⇒ iRk)
Proof
Definitions occuring in Statement :
dl_KS: dl_KS,
KrRel: sRt,
worlds: worlds(k),
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
Lemmas referenced :
Rtrans_wf,
KrRel_wf,
dl_KS_subtype,
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,j,k:worlds(K). (iRj {}\mRightarrow{} jRk {}\mRightarrow{} iRk)
Date html generated:
2019_10_16-AM-11_23_50
Last ObjectModification:
2019_04_26-PM-04_48_30
Theory : dynamic!logic
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