Nuprl Lemma : rmin-rleq-rmax
∀a,b:ℝ. (rmin(a;b) ≤ rmax(a;b))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmin: rmin(x;y),
rmax: rmax(x;y),
real: ℝ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
or: P ∨ Q,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
rmin_lb,
rleq-rmax,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
independent_isectElimination,
inlFormation,
productElimination,
hypothesis
Latex:
\mforall{}a,b:\mBbbR{}. (rmin(a;b) \mleq{} rmax(a;b))
Date html generated:
2016_05_18-AM-07_17_15
Last ObjectModification:
2015_12_28-AM-00_44_22
Theory : reals
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