Nuprl Lemma : vec-midpoint_wf
∀[n:ℕ]. ∀[a,b:ℝ^n]. (vec-midpoint(a;b) ∈ ℝ^n)
Proof
Definitions occuring in Statement :
vec-midpoint: vec-midpoint(a;b),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vec-midpoint: vec-midpoint(a;b),
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ
Lemmas referenced :
real-vec-mul_wf,
real-vec-add_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
rless_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
hypothesis,
natural_numberEquality,
independent_isectElimination,
inrFormation,
dependent_functionElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbR{}\^{}n]. (vec-midpoint(a;b) \mmember{} \mBbbR{}\^{}n)
Date html generated:
2016_10_28-AM-07_42_32
Last ObjectModification:
2016_09_28-PM-04_08_57
Theory : reals!model!euclidean!geometry
Home
Index