Nuprl Lemma : not-real-vec-sep-refl
∀[n:ℕ]. ∀[a:ℝ^n]. (¬a ≠ a)
Proof
Definitions occuring in Statement :
real-vec-sep: a ≠ b,
real-vec: ℝ^n,
nat: ℕ,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q),
uimplies: b supposing a
Lemmas referenced :
real-vec-sep_wf,
real-vec_wf,
nat_wf,
not-real-vec-sep-iff-eq,
req-vec_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
productElimination,
independent_isectElimination
Latex:
\mforall{}[n:\mBbbN{}]. \mforall{}[a:\mBbbR{}\^{}n]. (\mneg{}a \mneq{} a)
Date html generated:
2016_10_26-AM-10_30_28
Last ObjectModification:
2016_09_25-PM-02_12_30
Theory : reals
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