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
Home
Index