Nuprl Lemma : select-cons-tl
∀[a,as:Top]. ∀[i:ℤ]. [a / as][i] ~ as[i - 1] supposing 0 < i
Proof
Definitions occuring in Statement :
select: L[n],
cons: [a / b],
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
subtract: n - m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
select: L[n],
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
top: Top,
so_apply: x[s1;s2],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
less_than: a < b,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
not: ¬A,
false: False,
prop: ℙ,
subtype_rel: A ⊆r B,
le: A ≤ B,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
has-value: (a)↓
Lemmas referenced :
spread_cons_lemma,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
less_than_wf,
less-iff-le,
add_functionality_wrt_le,
add-associates,
add-zero,
add-commutes,
le-add-cancel2,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
value-type-has-value,
int-value-type,
subtract_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isectElimination,
hypothesisEquality,
natural_numberEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
independent_isectElimination,
lessCases,
isect_memberFormation,
sqequalAxiom,
because_Cache,
independent_pairFormation,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
addEquality,
applyEquality,
lambdaEquality,
intEquality,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
callbyvalueReduce
Latex:
\mforall{}[a,as:Top]. \mforall{}[i:\mBbbZ{}]. [a / as][i] \msim{} as[i - 1] supposing 0 < i
Date html generated:
2017_04_14-AM-08_36_40
Last ObjectModification:
2017_02_27-PM-03_28_26
Theory : list_0
Home
Index