Nuprl Lemma : rmax-idempotent
∀[x:ℝ]. (rmax(x;x) = x)
Proof
Definitions occuring in Statement :
rmax: rmax(x;y),
req: x = y,
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
cand: A c∧ B,
uiff: uiff(P;Q),
uimplies: b supposing a,
implies: P ⇒ Q
Lemmas referenced :
rmax_lb,
rleq_weakening_equal,
rleq-rmax,
rleq_antisymmetry,
req_witness,
rmax_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
productElimination,
independent_isectElimination,
hypothesis,
independent_pairFormation,
hypothesisEquality,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (rmax(x;x) = x)
Date html generated:
2016_05_18-AM-07_19_53
Last ObjectModification:
2015_12_28-AM-00_46_50
Theory : reals
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