Nuprl Lemma : uniform-continuity-pi-pi-prop
∀[T:Type]. ∀[F:(ℕ ⟶ 𝔹) ⟶ T]. ∀[n,m:ℕ]. (n = m ∈ ℕ) supposing (ucpB(T;F;m) and ucpB(T;F;n))
Proof
Definitions occuring in Statement :
uniform-continuity-pi-pi: ucpB(T;F;n),
nat: ℕ,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uniform-continuity-pi-pi: ucpB(T;F;n),
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
ge: i ≥ j ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
and: P ∧ Q
Lemmas referenced :
int_term_value_constant_lemma,
itermConstant_wf,
int_formula_prop_eq_lemma,
intformeq_wf,
int_formula_prop_and_lemma,
intformand_wf,
decidable__equal_int,
bool_wf,
nat_wf,
uniform-continuity-pi-pi_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_or_lemma,
int_formula_prop_not_lemma,
intformle_wf,
itermVar_wf,
intformless_wf,
intformor_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__le,
decidable__lt,
le_wf,
less_than_wf,
decidable__or,
nat_properties
Rules used in proof :
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
productElimination,
thin,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
functionEquality,
universeEquality,
isect_memberFormation,
introduction,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
independent_pairFormation,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} T]. \mforall{}[n,m:\mBbbN{}]. (n = m) supposing (ucpB(T;F;m) and ucpB(T;F;n))
Date html generated:
2016_05_14-PM-09_39_03
Last ObjectModification:
2016_01_15-PM-10_56_27
Theory : continuity
Home
Index