Nuprl Lemma : real-vec-between-symmetry
∀n:ℕ. ∀a,b,c:ℝ^n. (a-b-c ⇒ c-b-a)
Proof
Definitions occuring in Statement :
real-vec-between: a-b-c,
real-vec: ℝ^n,
nat: ℕ,
all: ∀x:A. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
real-vec-between: a-b-c,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
cand: A c∧ B,
prop: ℙ,
top: Top,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
uiff: uiff(P;Q),
uimplies: b supposing a,
rsub: x - y,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
rsub_wf,
int-to-real_wf,
i-member_wf,
rooint_wf,
req-vec_wf,
real-vec-add_wf,
real-vec-mul_wf,
real-vec-between_wf,
real-vec_wf,
nat_wf,
member_rooint_lemma,
radd-preserves-rless,
trivial-rsub-rless,
radd_wf,
rminus_wf,
rless_wf,
rless_functionality,
req_weakening,
radd-zero-both,
radd_functionality,
radd-rminus-both,
radd_comm,
radd-ac,
req_wf,
rmul_wf,
uiff_transitivity,
req_functionality,
rminus-radd,
rmul-int,
rmul_functionality,
rminus-as-rmul,
req_transitivity,
req_inversion,
rminus-rminus,
radd-assoc,
radd-int,
req-vec_functionality,
req-vec_weakening,
real-vec-add_functionality,
real-vec-mul_functionality,
real-vec-add-com
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
introduction,
extract_by_obid,
isectElimination,
natural_numberEquality,
hypothesis,
hypothesisEquality,
independent_pairFormation,
productEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_functionElimination,
independent_isectElimination,
addLevel,
levelHypothesis,
sqequalRule,
minusEquality,
multiplyEquality,
because_Cache,
addEquality
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c:\mBbbR{}\^{}n. (a-b-c {}\mRightarrow{} c-b-a)
Date html generated:
2016_10_26-AM-10_18_03
Last ObjectModification:
2016_09_24-PM-09_50_28
Theory : reals
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