Nuprl Lemma : l_before_wf
∀[T:Type]. ∀[l:T List]. ∀[x,y:T]. (x before y ∈ l ∈ ℙ)
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l_before: x before y ∈ l
Lemmas referenced :
sublist_wf,
cons_wf,
nil_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
Error :universeIsType,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[x,y:T]. (x before y \mmember{} l \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-01_23_05
Last ObjectModification:
2018_09_26-PM-05_23_33
Theory : list_1
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