Nuprl Lemma : rv-mul-sep2
∀rv:RealVectorSpace. ∀a:ℝ. ∀x,y:Point. (a*x # a*y ⇒ x # y)
Proof
Definitions occuring in Statement :
rv-mul: a*x,
real-vector-space: RealVectorSpace,
ss-sep: x # y,
ss-point: Point,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
top: Top,
not: ¬A,
exists: ∃x:A. B[x],
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
and: P ∧ Q,
squash: ↓T,
less_than: a < b,
nat_plus: ℕ+,
false: False,
sq_exists: ∃x:{A| B[x]},
rless: x < y,
rneq: x ≠ y,
or: P ∨ Q,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformless_wf,
satisfiable-full-omega-tt,
nat_plus_properties,
real-vector-space_wf,
real_wf,
ss-point_wf,
rv-mul_wf,
real-vector-space_subtype1,
ss-sep_wf,
rv-mul-sep
Rules used in proof :
independent_functionElimination,
computeAll,
voidEquality,
voidElimination,
isect_memberEquality,
intEquality,
int_eqEquality,
lambdaEquality,
dependent_pairFormation,
independent_isectElimination,
natural_numberEquality,
productElimination,
imageElimination,
rename,
setElimination,
unionElimination,
because_Cache,
sqequalRule,
applyEquality,
isectElimination,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
hypothesis,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
extract_by_obid,
introduction,
cut
Latex:
\mforall{}rv:RealVectorSpace. \mforall{}a:\mBbbR{}. \mforall{}x,y:Point. (a*x \# a*y {}\mRightarrow{} x \# y)
Date html generated:
2016_11_08-AM-09_13_45
Last ObjectModification:
2016_11_02-PM-00_48_10
Theory : inner!product!spaces
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