Nuprl Lemma : rneq_irreflexivity
∀[e:ℝ]. False supposing e ≠ e
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
rneq: x ≠ y,
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
rless_irreflexivity,
rneq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_isectElimination,
hypothesis,
voidElimination,
because_Cache,
sqequalRule,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[e:\mBbbR{}]. False supposing e \mneq{} e
Date html generated:
2016_05_18-AM-07_10_47
Last ObjectModification:
2015_12_28-AM-00_39_09
Theory : reals
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