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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