Nuprl Lemma : rmetric_wf
rmetric() ∈ metric(ℝ)
Proof
Definitions occuring in Statement :
rmetric: rmetric(),
metric: metric(X),
real: ℝ,
member: t ∈ T
Definitions unfolded in proof :
rmetric: rmetric(),
member: t ∈ T,
uall: ∀[x:A]. B[x],
metric: metric(X),
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
prop: ℙ,
uimplies: b supposing a,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
false: False,
absval: |i|,
req_int_terms: t1 ≡ t2
Lemmas referenced :
rabs_wf,
rsub_wf,
real_wf,
zero-rleq-rabs,
rleq_wf,
int-to-real_wf,
radd_wf,
req_wf,
rabs-difference-symmetry,
r-triangle-inequality2,
rleq_functionality,
req_weakening,
radd_functionality,
itermSubtract_wf,
itermVar_wf,
itermConstant_wf,
req-int,
decidable__equal_int,
full-omega-unsat,
intformnot_wf,
intformeq_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
req_functionality,
req_transitivity,
rabs_functionality,
rabs-int,
req-iff-rsub-is-0,
real_polynomial_null,
real_term_value_sub_lemma,
real_term_value_var_lemma,
real_term_value_const_lemma
Rules used in proof :
cut,
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaEquality_alt,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
inhabitedIsType,
universeIsType,
dependent_set_memberEquality_alt,
equalityTransitivity,
equalitySymmetry,
lambdaFormation_alt,
independent_pairFormation,
because_Cache,
productIsType,
functionIsType,
natural_numberEquality,
applyEquality,
independent_isectElimination,
productElimination,
minusEquality,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
isect_memberEquality_alt,
voidElimination,
int_eqEquality
Latex:
rmetric() \mmember{} metric(\mBbbR{})
Date html generated:
2019_10_29-AM-11_03_11
Last ObjectModification:
2019_10_02-AM-09_44_02
Theory : reals
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