Nuprl Lemma : sublist_iseg
∀[T:Type]. ∀L1,L2:T List.  (L1 ≤ L2 
⇒ L1 ⊆ L2)
Proof
Definitions occuring in Statement : 
iseg: l1 ≤ l2
, 
sublist: L1 ⊆ L2
, 
list: T List
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
universe: Type
Definitions unfolded in proof : 
iseg: l1 ≤ l2
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
exists: ∃x:A. B[x]
, 
member: t ∈ T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
length_wf_nat, 
equal_wf, 
nat_wf, 
iseg_is_sublist, 
iseg_append0, 
sublist_wf, 
exists_wf, 
append_wf, 
list_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
productElimination, 
thin, 
cut, 
dependent_set_memberEquality, 
hypothesis, 
introduction, 
extract_by_obid, 
isectElimination, 
cumulativity, 
hypothesisEquality, 
dependent_functionElimination, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
hyp_replacement, 
Error :applyLambdaEquality, 
setElimination, 
rename, 
because_Cache, 
lambdaEquality, 
universeEquality
Latex:
\mforall{}[T:Type].  \mforall{}L1,L2:T  List.    (L1  \mleq{}  L2  {}\mRightarrow{}  L1  \msubseteq{}  L2)
Date html generated:
2016_10_21-AM-10_08_01
Last ObjectModification:
2016_07_12-AM-05_27_04
Theory : list_1
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