Nuprl Lemma : select_cons_tl_sq
∀[T:Type]. ∀[x:T]. ∀[l:T List]. ∀[i:ℕ||l||]. ([x / l][i + 1] ~ l[i])
Proof
Definitions occuring in Statement :
select: L[n],
length: ||as||,
cons: [a / b],
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
add: n + m,
natural_number: $n,
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
int_seg: {i..j-},
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
lelt: i ≤ j < k,
subtract: n - m,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
select-cons-tl,
decidable__lt,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
add-subtract-cancel,
int_seg_wf,
length_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
cut,
lemma_by_obid,
sqequalHypSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
independent_isectElimination,
dependent_functionElimination,
hypothesis,
unionElimination,
independent_pairFormation,
lambdaFormation,
productElimination,
independent_functionElimination,
applyEquality,
lambdaEquality,
intEquality,
because_Cache,
minusEquality,
universeEquality,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[l:T List]. \mforall{}[i:\mBbbN{}||l||]. ([x / l][i + 1] \msim{} l[i])
Date html generated:
2016_05_14-AM-06_36_33
Last ObjectModification:
2015_12_26-PM-00_33_55
Theory : list_0
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