Nuprl Lemma : member_nth_tl
∀[T:Type]. ∀n:ℕ. ∀x:T. ∀L:T List. ((x ∈ nth_tl(n;L)) ⇒ (x ∈ L))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
nth_tl: nth_tl(n;as),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
nat: ℕ,
nth_tl: nth_tl(n;as),
le_int: i ≤z j,
lt_int: i <z j,
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
subtype_rel: A ⊆r B,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
all_wf,
list_wf,
l_member_wf,
nth_tl_wf,
subtract_wf,
set_wf,
less_than_wf,
primrec-wf2,
nat_wf,
list_induction,
nth_tl_nil,
nil_wf,
le_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
lt_int_wf,
bnot_wf,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf,
cons_wf,
reduce_tl_cons_lemma,
cons_member
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
rename,
setElimination,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
functionEquality,
natural_numberEquality,
intEquality,
universeEquality,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
equalityTransitivity,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
inrFormation
Latex:
\mforall{}[T:Type]. \mforall{}n:\mBbbN{}. \mforall{}x:T. \mforall{}L:T List. ((x \mmember{} nth\_tl(n;L)) {}\mRightarrow{} (x \mmember{} L))
Date html generated:
2018_05_21-PM-06_30_01
Last ObjectModification:
2017_07_26-PM-04_50_20
Theory : general
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