Nuprl Lemma : member_rcoint_lemma
∀r,u,l:Top. (r ∈ [l, u) ~ (l ≤ r) ∧ (r < u))
Proof
Definitions occuring in Statement :
rcoint: [l, u),
i-member: r ∈ I,
rleq: x ≤ y,
rless: x < y,
top: Top,
all: ∀x:A. B[x],
and: P ∧ Q,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
rcoint: [l, u),
i-member: r ∈ I
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
lemma_by_obid,
sqequalRule
Latex:
\mforall{}r,u,l:Top. (r \mmember{} [l, u) \msim{} (l \mleq{} r) \mwedge{} (r < u))
Date html generated:
2016_05_18-AM-08_20_30
Last ObjectModification:
2015_12_27-PM-11_55_35
Theory : reals
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