Nuprl Lemma : locally-non-constant-rational_wf
∀[a,b,c:ℝ]. ∀[f:[a, b] ⟶ℝ]. (locally-non-constant-rational(f;a;b;c) ∈ ℙ)
Proof
Definitions occuring in Statement :
locally-non-constant-rational: locally-non-constant-rational(f;a;b;c),
rfun: I ⟶ℝ,
rccint: [l, u],
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
locally-non-constant-rational: locally-non-constant-rational(f;a;b;c),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
int_nzero: ℤ-o,
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
nequal: a ≠ b ∈ T ,
not: ¬A,
false: False,
guard: {T},
rless: x < y,
sq_exists: ∃x:{A| B[x]},
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
i-member: r ∈ I,
rccint: [l, u]
Lemmas referenced :
rfun_wf,
rleq_transitivity,
rccint_wf,
r-ap_wf,
rneq_wf,
int-to-real_wf,
equal_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformand_wf,
satisfiable-full-omega-tt,
nat_plus_properties,
nequal_wf,
less_than_wf,
subtype_rel_sets,
int-rdiv_wf,
nat_plus_wf,
exists_wf,
rless_wf,
rleq_wf,
real_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
functionEquality,
hypothesisEquality,
intEquality,
productEquality,
applyEquality,
natural_numberEquality,
independent_isectElimination,
setElimination,
rename,
setEquality,
lambdaFormation,
dependent_pairFormation,
int_eqEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
independent_functionElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b,c:\mBbbR{}]. \mforall{}[f:[a, b] {}\mrightarrow{}\mBbbR{}]. (locally-non-constant-rational(f;a;b;c) \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-09_24_29
Last ObjectModification:
2016_01_17-AM-02_42_36
Theory : reals
Home
Index