Nuprl Lemma : mkr2_wf
∀[a,b:ℝ]. (mkr2(a;b) ∈ ℝ^2)
Proof
Definitions occuring in Statement :
mkr2: mkr2(a;b),
real-vec: ℝ^n,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
mkr2: mkr2(a;b),
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
select_wf,
real_wf,
cons_wf,
nil_wf,
int_seg_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
hypothesisEquality,
setElimination,
rename,
independent_isectElimination,
natural_numberEquality,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
addEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbR{}]. (mkr2(a;b) \mmember{} \mBbbR{}\^{}2)
Date html generated:
2017_10_05-AM-00_12_49
Last ObjectModification:
2017_04_10-PM-10_02_40
Theory : inner!product!spaces
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