Nuprl Lemma : sublist-rec-iff-sublist
∀[T:Type]. ∀l1,l2:T List. (l1 ⊆ l2 ⇐⇒ sublist-rec(T;l1;l2))
Proof
Definitions occuring in Statement :
sublist-rec: sublist-rec(T;l1;l2),
sublist: L1 ⊆ L2,
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],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
or: P ∨ Q,
sublist-rec: sublist-rec(T;l1;l2),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
true: True,
cons: [a / b],
false: False,
cand: A c∧ B,
guard: {T}
Lemmas referenced :
list_induction,
all_wf,
list_wf,
iff_wf,
sublist_wf,
sublist-rec_wf,
nil_wf,
sublist_nil,
cons_wf,
list-cases,
list_ind_nil_lemma,
product_subtype_list,
cons_sublist_nil,
list_ind_cons_lemma,
cons_sublist_cons,
and_wf,
equal_wf,
nil_sublist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
independent_pairFormation,
because_Cache,
dependent_functionElimination,
productElimination,
rename,
universeEquality,
unionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
inlFormation,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}l1,l2:T List. (l1 \msubseteq{} l2 \mLeftarrow{}{}\mRightarrow{} sublist-rec(T;l1;l2))
Date html generated:
2016_05_15-PM-03_34_01
Last ObjectModification:
2015_12_27-PM-01_13_18
Theory : general
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