Nuprl Lemma : sublist-reverse
∀[T:Type]. ∀L1,L2:T List. (rev(L1) ⊆ rev(L2) ⇐⇒ L1 ⊆ L2)
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
reverse: rev(as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
top: Top,
false: False,
iff: P ⇐⇒ Q,
and: P ∧ Q,
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B
Lemmas referenced :
list_induction,
all_wf,
list_wf,
sublist_wf,
reverse_wf,
reverse_nil_lemma,
reverse-cons,
nil-sublist,
nil_wf,
cons_wf,
append_wf,
false_wf,
cons_sublist_nil,
or_wf,
equal_wf,
cons_sublist_cons,
sublist_append,
sublist_weakening,
sublist_transitivity,
sublist_append1,
reverse-reverse,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
universeEquality,
cut,
lambdaFormation,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
functionEquality,
independent_functionElimination,
rename,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
dependent_functionElimination,
addLevel,
impliesFunctionality,
productElimination,
unionElimination,
productEquality,
independent_isectElimination,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
independent_pairFormation,
applyEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. (rev(L1) \msubseteq{} rev(L2) \mLeftarrow{}{}\mRightarrow{} L1 \msubseteq{} L2)
Date html generated:
2017_04_17-AM-08_52_46
Last ObjectModification:
2017_02_27-PM-05_08_24
Theory : list_1
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