Nuprl Lemma : vec-midpoint-symmetry
∀[n:ℕ]. ∀[a,b:ℝ^n]. req-vec(n;vec-midpoint(b;a);vec-midpoint(a;b))
Proof
Definitions occuring in Statement :
vec-midpoint: vec-midpoint(a;b),
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
vec-midpoint: vec-midpoint(a;b),
req-vec: req-vec(n;x;y),
real-vec-add: X + Y,
real-vec-mul: a*X,
all: ∀x:A. B[x],
nat: ℕ,
subtype_rel: A ⊆r B,
real-vec: ℝ^n,
implies: P ⇒ Q,
uimplies: b supposing a,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ
Lemmas referenced :
int_seg_wf,
req_witness,
vec-midpoint_wf,
real-vec_wf,
nat_wf,
rdiv_wf,
int-to-real_wf,
rless-int,
rless_wf,
radd_wf,
req_weakening,
radd_comm,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
dependent_functionElimination,
applyEquality,
independent_functionElimination,
isect_memberEquality,
because_Cache,
independent_isectElimination,
inrFormation,
productElimination,
independent_pairFormation,
imageMemberEquality,
baseClosed
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a,b:\mBbbR{}\^{}n]. req-vec(n;vec-midpoint(b;a);vec-midpoint(a;b))
Date html generated:
2016_10_28-AM-07_42_40
Last ObjectModification:
2016_09_28-PM-04_29_13
Theory : reals!model!euclidean!geometry
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