Nuprl Lemma : cons-listp
∀[T:Type]. ∀[l:T List]. ∀[x:T]. ([x / l] ∈ T List+)
Proof
Definitions occuring in Statement :
listp: A List+,
cons: [a / b],
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
top: Top,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
nat: ℕ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
listp: A List+,
prop: ℙ,
ge: i ≥ j ,
subtract: n - m,
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
true: True,
decidable: Dec(P),
or: P ∨ Q
Lemmas referenced :
length_of_cons_lemma,
istype-void,
length_wf_nat,
set_subtype_base,
le_wf,
istype-int,
int_subtype_base,
cons_wf,
less_than_wf,
length_wf,
list_wf,
add-commutes,
add_functionality_wrt_le,
subtract_wf,
le_reflexive,
minus-one-mul,
zero-add,
one-mul,
add-mul-special,
add-associates,
two-mul,
mul-distributes-right,
zero-mul,
not-lt-2,
minus-zero,
add-zero,
add-swap,
omega-shadow,
nat_properties,
decidable__lt
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
Error :isect_memberEquality_alt,
voidElimination,
hypothesis,
isectElimination,
hypothesisEquality,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
Error :dependent_pairFormation_alt,
Error :universeIsType,
sqequalIntensionalEquality,
applyEquality,
intEquality,
Error :lambdaEquality_alt,
natural_numberEquality,
independent_isectElimination,
because_Cache,
Error :equalityIsType1,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
productElimination,
promote_hyp,
Error :dependent_set_memberEquality_alt,
axiomEquality,
universeEquality,
multiplyEquality,
addEquality,
minusEquality,
independent_pairFormation,
imageMemberEquality,
baseClosed,
setElimination,
rename,
unionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[x:T]. ([x / l] \mmember{} T List\msupplus{})
Date html generated:
2019_06_20-PM-00_40_23
Last ObjectModification:
2018_10_03-PM-02_06_12
Theory : list_0
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