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-},
ge: i ≥ j ,
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
nat_wf,
list_wf,
strong-type-continuous_wf,
false_wf,
le_wf,
nat_properties,
length_wf_nat,
equal_wf,
select_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
int_seg_wf,
length_wf,
ge_wf,
less_than_wf,
subtract_wf,
itermSubtract_wf,
int_term_value_subtract_lemma,
first0,
subtype_rel_list,
top_wf,
nil_wf,
firstn_decomp,
append_wf,
cons_wf,
lelt_wf,
firstn_all
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,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
computeAll,
intWeakElimination,
comment
Latex:
\mforall{}[F:Type {}\mrightarrow{} Type]. Continuous+(T.F[T] List) supposing Continuous+(T.F[T])
Date html generated:
2017_04_17-AM-08_49_32
Last ObjectModification:
2017_02_27-PM-05_07_59
Theory : list_1
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