Nuprl Lemma : rcp_wf
∀[a,b:ℝ^3]. ((a x b) ∈ ℝ^3)
Proof
Definitions occuring in Statement :
rcp: (a x b),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n
Definitions unfolded in proof :
rcp: (a x b),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
uimplies: b supposing a,
guard: {T},
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
select_wf,
real_wf,
cons_wf,
rsub_wf,
rmul_wf,
int_seg_wf,
false_wf,
lelt_wf,
nil_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
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
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
because_Cache,
applyEquality,
functionExtensionality,
hypothesisEquality,
natural_numberEquality,
dependent_set_memberEquality,
independent_pairFormation,
lambdaFormation,
imageMemberEquality,
baseClosed,
setElimination,
rename,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
addEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[a,b:\mBbbR{}\^{}3]. ((a x b) \mmember{} \mBbbR{}\^{}3)
Date html generated:
2018_05_22-PM-02_39_20
Last ObjectModification:
2018_05_09-PM-00_53_50
Theory : reals
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