Nuprl Lemma : iseg_transitivity2
∀[T:Type]. ∀l1,l2,l3:T List. (l2 ≤ l3 ⇒ l1 ≤ l2 ⇒ l1 ≤ l3)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
iseg_transitivity,
iseg_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2,l3:T List. (l2 \mleq{} l3 {}\mRightarrow{} l1 \mleq{} l2 {}\mRightarrow{} l1 \mleq{} l3)
Date html generated:
2019_06_20-PM-01_28_24
Last ObjectModification:
2018_09_26-PM-05_39_34
Theory : list_1
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