Nuprl Lemma : l_before_sublist
∀[T:Type]. ∀L1,L2:T List. (L1 ⊆ L2 ⇒ {∀x,y:T. (x before y ∈ L1 ⇒ x before y ∈ L2)})
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
sublist: L1 ⊆ L2,
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
guard: {T},
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ
Lemmas referenced :
sublist_transitivity,
cons_wf,
nil_wf,
sublist_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
hypothesis,
independent_functionElimination,
Error :universeIsType,
Error :inhabitedIsType,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (L1 \msubseteq{} L2 {}\mRightarrow{} \{\mforall{}x,y:T. (x before y \mmember{} L1 {}\mRightarrow{} x before y \mmember{} L2)\})
Date html generated:
2019_06_20-PM-01_23_28
Last ObjectModification:
2018_09_29-PM-00_28_14
Theory : list_1
Home
Index