Nuprl Lemma : proper-real-continuity_wf
proper-real-continuity() ∈ ℙ
Proof
Definitions occuring in Statement :
proper-real-continuity: proper-real-continuity(),
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
not: ¬A,
false: False,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
sq_exists: ∃x:{A| B[x]},
rless: x < y,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
or: P ∨ Q,
guard: {T},
rneq: x ≠ y,
uimplies: b supposing a,
nat_plus: ℕ+,
rfun: I ⟶ℝ,
and: P ∧ Q,
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
all: ∀x:A. B[x],
proper-real-continuity: proper-real-continuity()
Lemmas referenced :
member_rccint_lemma,
all_wf,
real_wf,
rless_wf,
rfun_wf,
rccint_wf,
nat_plus_wf,
sq_exists_wf,
int-to-real_wf,
rleq_wf,
rabs_wf,
rsub_wf,
and_wf,
rdiv_wf,
rless-int,
nat_plus_properties,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
computeAll,
independent_pairFormation,
intEquality,
int_eqEquality,
dependent_pairFormation,
unionElimination,
independent_functionElimination,
inrFormation,
productElimination,
independent_isectElimination,
rename,
setElimination,
dependent_set_memberEquality,
applyEquality,
natural_numberEquality,
productEquality,
because_Cache,
hypothesisEquality,
functionEquality,
lambdaEquality,
isectElimination,
hypothesis,
voidEquality,
voidElimination,
isect_memberEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
proper-real-continuity() \mmember{} \mBbbP{}
Date html generated:
2016_05_18-AM-10_52_28
Last ObjectModification:
2016_01_17-AM-00_13_39
Theory : reals
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