Nuprl Lemma : select-cons-hd
∀[a,as:Top]. ∀[i:ℤ]. [a / as][i] ~ a supposing i ≤ 0
Proof
Definitions occuring in Statement :
select: L[n],
cons: [a / b],
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
le: A ≤ B,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
select: L[n],
subtract: n - m,
cons: [a / b],
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
squash: ↓T,
not: ¬A,
false: False,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
le: A ≤ B
Lemmas referenced :
decidable__lt,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
less_than_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
not-lt-2,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
le_wf,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
unionElimination,
isectElimination,
lambdaFormation,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
lessCases,
sqequalAxiom,
isect_memberEquality,
independent_pairFormation,
voidElimination,
voidEquality,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination,
dependent_pairFormation,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
instantiate,
cumulativity,
intEquality
Latex:
\mforall{}[a,as:Top]. \mforall{}[i:\mBbbZ{}]. [a / as][i] \msim{} a supposing i \mleq{} 0
Date html generated:
2017_04_14-AM-08_36_35
Last ObjectModification:
2017_02_27-PM-03_28_24
Theory : list_0
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