Nuprl Lemma : list_subtype_base
∀[A:Type]. (A List) ⊆r Base supposing A ⊆r Base
Proof
Definitions occuring in Statement :
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
base: Base,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
prop: ℙ,
or: P ∨ Q,
nil: [],
cons: [a / b],
colength: colength(L),
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
squash: ↓T,
sq_stable: SqStable(P),
uiff: uiff(P;Q),
and: P ∧ Q,
le: A ≤ B,
not: ¬A,
less_than': less_than'(a;b),
true: True,
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
subtract: n - m
Lemmas referenced :
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
list-cases,
product_subtype_list,
spread_cons_lemma,
istype-void,
colength_wf_list,
sq_stable__le,
le_antisymmetry_iff,
add_functionality_wrt_le,
add-associates,
istype-int,
add-zero,
zero-add,
le-add-cancel,
int_subtype_base,
le_wf,
subtract-1-ge-0,
subtype_base_sq,
nat_wf,
set_subtype_base,
add-commutes,
add-swap,
product_subtype_base,
base_wf,
subtype_rel_self,
le_weakening2,
list_wf,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaEquality_alt,
thin,
Error :lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
sqequalRule,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
voidElimination,
Error :universeIsType,
dependent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
unionElimination,
baseClosed,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :isect_memberEquality_alt,
applyLambdaEquality,
imageMemberEquality,
imageElimination,
addEquality,
applyEquality,
because_Cache,
Error :equalityIsType4,
Error :equalityIsType1,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
instantiate,
cumulativity,
intEquality,
minusEquality,
independent_pairEquality,
universeEquality
Latex:
\mforall{}[A:Type]. (A List) \msubseteq{}r Base supposing A \msubseteq{}r Base
Date html generated:
2019_06_20-PM-00_38_43
Last ObjectModification:
2018_10_03-PM-06_54_58
Theory : list_0
Home
Index