Nuprl Lemma : m-unif-cont_wf
∀[X:Type]. ∀[dx:metric(X)]. ∀[Y:Type]. ∀[dy:metric(Y)]. ∀[f:X ⟶ Y]. (UC(f:X ⟶ Y) ∈ ℙ)
Proof
Definitions occuring in Statement :
m-unif-cont: UC(f:X ⟶ Y),
metric: metric(X),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s],
top: Top,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
decidable: Dec(P),
sq_exists: ∃x:A [B[x]],
rless: x < y,
rev_implies: P ⇐ Q,
and: P ∧ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
guard: {T},
rneq: x ≠ y,
uimplies: b supposing a,
nat_plus: ℕ+,
implies: P ⇒ Q,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
m-unif-cont: UC(f:X ⟶ Y),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
metric_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_less_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__lt,
nat_plus_properties,
rless-int,
rdiv_wf,
mdist_wf,
rleq_wf,
int-to-real_wf,
rless_wf,
real_wf,
exists_wf,
nat_plus_wf,
all_wf
Rules used in proof :
universeEquality,
instantiate,
inhabitedIsType,
isectIsTypeImplies,
functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
setIsType,
independent_pairFormation,
voidElimination,
isect_memberEquality_alt,
int_eqEquality,
dependent_pairFormation_alt,
approximateComputation,
unionElimination,
independent_functionElimination,
productElimination,
dependent_functionElimination,
inrFormation_alt,
independent_isectElimination,
applyEquality,
functionEquality,
because_Cache,
rename,
setElimination,
universeIsType,
lambdaFormation_alt,
hypothesisEquality,
natural_numberEquality,
setEquality,
closedConclusion,
lambdaEquality_alt,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[X:Type]. \mforall{}[dx:metric(X)]. \mforall{}[Y:Type]. \mforall{}[dy:metric(Y)]. \mforall{}[f:X {}\mrightarrow{} Y]. (UC(f:X {}\mrightarrow{} Y) \mmember{} \mBbbP{})
Date html generated:
2019_10_30-AM-06_36_07
Last ObjectModification:
2019_10_25-PM-01_57_26
Theory : reals
Home
Index