Nuprl Lemma : rv-be-symmetry
∀n:ℕ. ∀a,b,c:ℝ^n. (a_b_c ⇒ c_b_a)
Proof
Definitions occuring in Statement :
rv-be: 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,
rv-be: a_b_c,
not: ¬A,
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
false: False,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real-vec-sep-symmetry,
real-vec-sep_wf,
not_wf,
rv-between_wf,
rv-be_wf,
real-vec_wf,
nat_wf,
rv-between-symmetry
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
introduction,
independent_functionElimination,
thin,
productElimination,
cut,
extract_by_obid,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
independent_pairFormation,
because_Cache,
voidElimination,
productEquality,
isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}a,b,c:\mBbbR{}\^{}n. (a\_b\_c {}\mRightarrow{} c\_b\_a)
Date html generated:
2017_10_03-AM-11_31_58
Last ObjectModification:
2017_08_12-PM-00_07_51
Theory : reals
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