Nuprl Lemma : rneq_wf
∀[x,y:ℝ]. (x ≠ y ∈ ℙ)
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
real: ℝ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
rneq: x ≠ y
Lemmas referenced :
or_wf,
rless_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[x,y:\mBbbR{}]. (x \mneq{} y \mmember{} \mBbbP{})
Date html generated:
2016_05_18-AM-07_10_22
Last ObjectModification:
2015_12_28-AM-00_38_34
Theory : reals
Home
Index