Nuprl Lemma : real-vec-sep_inversion
∀n:ℕ. ∀x,y:ℝ^n. (x ≠ y ⇒ y ≠ x)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
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,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
real-vec-sep-symmetry,
real-vec-sep_wf,
real-vec_wf,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_functionElimination,
hypothesis,
isectElimination
Latex:
\mforall{}n:\mBbbN{}. \mforall{}x,y:\mBbbR{}\^{}n. (x \mneq{} y {}\mRightarrow{} y \mneq{} x)
Date html generated:
2017_10_03-AM-10_59_26
Last ObjectModification:
2017_04_07-PM-02_24_27
Theory : reals
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