Nuprl Lemma : continuous-id
∀[I:Interval]. x continuous for x ∈ I
Proof
Definitions occuring in Statement :
continuous: f[x] continuous for x ∈ I,
interval: Interval,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
continuous: f[x] continuous for x ∈ I,
all: ∀x:A. B[x],
sq_exists: ∃x:{A| B[x]},
member: t ∈ T,
nat_plus: ℕ+,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
interval_wf,
icompact_wf,
set_wf,
nat_plus_wf,
less_than_wf,
all_wf,
real_wf,
i-approx_wf,
i-member_wf,
rsub_wf,
rabs_wf,
rleq_wf,
int_term_value_mul_lemma,
itermMultiply_wf,
rless-int-fractions2,
rless_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,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformless_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
nat_plus_properties,
rless-int,
int-to-real_wf,
rdiv_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_set_memberFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
setElimination,
rename,
hypothesisEquality,
independent_isectElimination,
sqequalRule,
inrFormation,
dependent_functionElimination,
because_Cache,
productElimination,
independent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
multiplyEquality,
productEquality,
functionEquality,
dependent_set_memberEquality
Latex:
\mforall{}[I:Interval]. x continuous for x \mmember{} I
Date html generated:
2016_05_18-AM-09_10_36
Last ObjectModification:
2016_01_17-AM-02_36_51
Theory : reals
Home
Index