Nuprl Lemma : strong-continuous-list
∀[F:Type ⟶ Type]. Continuous+(T.F[T] List) supposing Continuous+(T.F[T])
Proof
Definitions occuring in Statement :
list: T List,
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
int_seg: {i..j-},
sq_stable: SqStable(P),
lelt: i ≤ j < k,
squash: ↓T,
or: P ∨ Q,
decidable: Dec(P),
top: Top,
exists: ∃x:A. B[x],
satisfiable_int_formula: Error :satisfiable_int_formula,
ge: i ≥ j ,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
subtract: n - m,
true: True,
gt: i > j
Lemmas referenced :
nat_wf,
list_wf,
strong-type-continuous_wf,
false_wf,
le_wf,
nat_properties,
length_wf_nat,
equal_wf,
select_wf,
sq_stable__le,
int_seg_wf,
length_wf,
Error :int_term_value_subtract_lemma,
Error :int_formula_prop_not_lemma,
Error :itermSubtract_wf,
Error :intformnot_wf,
subtract_wf,
decidable__le,
less_than_wf,
ge_wf,
Error :int_formula_prop_wf,
Error :int_formula_prop_less_lemma,
Error :int_term_value_var_lemma,
Error :int_term_value_constant_lemma,
Error :int_formula_prop_le_lemma,
Error :int_formula_prop_and_lemma,
Error :intformless_wf,
Error :itermVar_wf,
Error :itermConstant_wf,
Error :intformle_wf,
Error :intformand_wf,
Error :satisfiable-full-omega-tt,
first0,
subtype_rel_list,
top_wf,
nil_wf,
decidable__lt,
firstn_decomp,
le_weakening2,
append_wf,
cons_wf,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-one-mul-top,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
add-zero,
le-add-cancel,
lelt_wf,
firstn_all,
not-gt-2,
not-lt-2,
le-add-cancel2,
le_reflexive
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
lambdaEquality,
isectEquality,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
functionExtensionality,
hypothesisEquality,
universeEquality,
isect_memberEquality,
productElimination,
independent_pairEquality,
axiomEquality,
functionEquality,
cumulativity,
because_Cache,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
dependent_set_memberEquality,
natural_numberEquality,
dependent_functionElimination,
independent_functionElimination,
setElimination,
rename,
independent_isectElimination,
imageMemberEquality,
baseClosed,
imageElimination,
unionElimination,
computeAll,
voidEquality,
voidElimination,
intEquality,
int_eqEquality,
dependent_pairFormation,
intWeakElimination,
addEquality,
minusEquality,
comment
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. Continuous+(T.F[T] List) supposing Continuous+(T.F[T])
Date html generated:
2018_05_21-PM-00_20_45
Last ObjectModification:
2017_10_18-PM-00_43_48
Theory : list_0
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