Nuprl Lemma : seq-cont-nat
∀F:(ℕ ⟶ ℕ) ⟶ ℕ. seq-cont(ℕ;F)
Proof
Definitions occuring in Statement :
seq-cont: seq-cont(T;F),
nat: ℕ,
all: ∀x:A. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
guard: {T},
exists: ∃x:A. B[x],
not: ¬A,
false: False,
less_than': less_than'(a;b),
le: A ≤ B,
uimplies: b supposing a,
so_apply: x[s],
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
seq-cont: seq-cont(T;F),
all: ∀x:A. B[x],
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
sq_type: SQType(T),
isl: isl(x),
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
squash: ↓T,
cand: A c∧ B,
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
int_upper: {i...},
outl: outl(x)
Lemmas referenced :
int_upper_subtype_nat,
int_upper_wf,
isl_wf,
assert_wf,
isect_wf,
subtype_rel_self,
false_wf,
int_seg_subtype_nat,
nat_wf,
subtype_rel_dep_function,
equal_wf,
all_wf,
unit_wf2,
int_seg_wf,
exists_wf,
implies-quotient-true,
strong-continuity2-no-inner-squash,
bool_subtype_base,
bool_wf,
subtype_base_sq,
btrue_wf,
and_wf,
iff_weakening_equal,
true_wf,
squash_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
intformle_wf,
intformand_wf,
decidable__le,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
full-omega-unsat,
btrue_neq_bfalse,
int_subtype_base,
subtype_rel-equal,
bfalse_wf,
decidable__equal_int,
nat_properties,
int_upper_properties
Rules used in proof :
productElimination,
independent_functionElimination,
inlEquality,
independent_pairFormation,
independent_isectElimination,
functionExtensionality,
applyEquality,
productEquality,
lambdaEquality,
sqequalRule,
unionEquality,
hypothesis,
rename,
setElimination,
natural_numberEquality,
because_Cache,
functionEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
dependent_pairFormation,
cumulativity,
instantiate,
applyLambdaEquality,
equalitySymmetry,
equalityTransitivity,
dependent_set_memberEquality,
baseClosed,
imageMemberEquality,
universeEquality,
imageElimination,
voidEquality,
isect_memberEquality,
int_eqEquality,
approximateComputation,
voidElimination,
intEquality,
promote_hyp,
unionElimination
Latex:
\mforall{}F:(\mBbbN{} {}\mrightarrow{} \mBbbN{}) {}\mrightarrow{} \mBbbN{}. seq-cont(\mBbbN{};F)
Date html generated:
2017_09_29-PM-06_05_48
Last ObjectModification:
2017_07_19-AM-11_24_59
Theory : continuity
Home
Index