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
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