Nuprl Lemma : K-le_transitivity
∀K:mKripkeStruct. ∀i,j,k:World.  (i ≤ j 
⇒ j ≤ k 
⇒ i ≤ k)
Proof
Definitions occuring in Statement : 
K-le: i ≤ j
, 
K-world: World
, 
mFO-Kripke-struct: mKripkeStruct
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
Definitions unfolded in proof : 
K-le: i ≤ j
, 
K-world: World
, 
all: ∀x:A. B[x]
, 
mFO-Kripke-struct: mKripkeStruct
, 
spreadn: spread4, 
pi1: fst(t)
, 
pi2: snd(t)
, 
and: P ∧ Q
, 
member: t ∈ T
Lemmas referenced : 
mFO-Kripke-struct_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
lambdaFormation_alt, 
sqequalHypSubstitution, 
productElimination, 
thin, 
hypothesis, 
universeIsType, 
cut, 
introduction, 
extract_by_obid
Latex:
\mforall{}K:mKripkeStruct.  \mforall{}i,j,k:World.    (i  \mleq{}  j  {}\mRightarrow{}  j  \mleq{}  k  {}\mRightarrow{}  i  \mleq{}  k)
Date html generated:
2019_10_16-AM-11_44_21
Last ObjectModification:
2018_10_13-AM-11_57_02
Theory : minimal-first-order-logic
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