Nuprl Lemma : not-rneq
∀[x,y:ℝ]. x = y supposing ¬x ≠ y
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
rneq: x ≠ y,
guard: {T},
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
rleq_antisymmetry,
not-rless,
rless_wf,
req_witness,
not_wf,
rneq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
because_Cache,
lambdaFormation,
hypothesis,
independent_functionElimination,
sqequalRule,
inrFormation,
inlFormation,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[x,y:\mBbbR{}]. x = y supposing \mneg{}x \mneq{} y
Date html generated:
2016_05_18-AM-07_13_16
Last ObjectModification:
2015_12_28-AM-00_40_45
Theory : reals
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