Nuprl Lemma : sqntype_list
∀[A:Type]. ∀[n:ℕ]. sqntype(n;A List) supposing sqntype(n;A)
Proof
Definitions occuring in Statement :
list: T List,
sqntype: sqntype(n;T),
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sqntype: sqntype(n;T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
false: False,
ge: i ≥ j ,
guard: {T},
subtype_rel: A ⊆r B,
or: P ∨ Q,
cons: [a / b],
top: Top,
and: P ∧ Q,
not: ¬A,
exists: ∃x:A. B[x],
uiff: uiff(P;Q),
subtract: n - m,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
label: ...$L... t,
sq_stable: SqStable(P)
Lemmas referenced :
sqntype_wf,
nat_wf,
length_wf_nat,
length_wf,
list_wf,
base_wf,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
subtract-1-ge-0,
int_subtype_base,
list-cases,
length_of_nil_lemma,
product_subtype_list,
null_nil_lemma,
btrue_wf,
null_cons_lemma,
istype-void,
bfalse_wf,
null_wf,
btrue_neq_bfalse,
length_of_cons_lemma,
le_weakening2,
non_neg_length,
le_antisymmetry_iff,
condition-implies-le,
minus-add,
istype-int,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
set_subtype_base,
le_wf,
subtract_wf,
add-associates,
minus-zero,
add-swap,
subtype_base_sq,
equal_wf,
squash_wf,
true_wf,
istype-universe,
tl_wf,
subtype_rel_self,
iff_weakening_equal,
length_tl,
decidable__le,
istype-false,
not-ge-2,
less-iff-le,
le-add-cancel2,
reduce_tl_nil_lemma,
le_weakening,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
subtype_rel_wf,
hd_wf,
decidable__lt,
sq_stable__le,
decidable__equal_int,
not-equal-2,
not-lt-2,
subtract-add-cancel,
sqequal_n_add,
not-le-2,
minus-minus
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
Error :lambdaEquality_alt,
dependent_functionElimination,
thin,
hypothesisEquality,
Error :axiomSqequalN,
hypothesis,
Error :functionIsTypeImplies,
Error :inhabitedIsType,
Error :universeIsType,
extract_by_obid,
isectElimination,
Error :isect_memberEquality_alt,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
Error :lambdaFormation_alt,
Error :equalityIsType1,
independent_functionElimination,
Error :equalityIsType4,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
voidElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
Error :productIsType,
Error :equalityIsType3,
applyLambdaEquality,
Error :dependent_pairFormation_alt,
sqequalIntensionalEquality,
addEquality,
minusEquality,
intEquality,
instantiate,
cumulativity,
sqequalnReflexivity,
imageElimination,
imageMemberEquality,
Error :equalityIsType2,
hyp_replacement,
sqequal_n rule,
sqequalZero
Latex:
\mforall{}[A:Type]. \mforall{}[n:\mBbbN{}]. sqntype(n;A List) supposing sqntype(n;A)
Date html generated:
2019_06_20-PM-00_44_19
Last ObjectModification:
2018_10_07-AM-00_39_05
Theory : list_0
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