Nuprl Lemma : rmin-max-cases
∀a,b:ℝ. (a ≠ b ⇒ (((rmin(a;b) = a) ∧ (rmax(a;b) = b)) ∨ ((rmin(a;b) = b) ∧ (rmax(a;b) = a))))
Proof
Definitions occuring in Statement :
rneq: x ≠ y,
rmin: rmin(x;y),
rmax: rmax(x;y),
req: x = y,
real: ℝ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
rneq: x ≠ y,
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
guard: {T},
prop: ℙ
Lemmas referenced :
rmin-req2,
rleq_weakening_rless,
rmax-req,
and_wf,
req_wf,
rmin_wf,
rmax_wf,
rmin-req,
rmax-req2,
rneq_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
thin,
inlFormation,
cut,
lemma_by_obid,
isectElimination,
because_Cache,
hypothesisEquality,
independent_isectElimination,
hypothesis,
independent_pairFormation,
sqequalRule,
inrFormation
Latex:
\mforall{}a,b:\mBbbR{}. (a \mneq{} b {}\mRightarrow{} (((rmin(a;b) = a) \mwedge{} (rmax(a;b) = b)) \mvee{} ((rmin(a;b) = b) \mwedge{} (rmax(a;b) = a))))
Date html generated:
2016_05_18-AM-07_15_57
Last ObjectModification:
2015_12_28-AM-00_43_46
Theory : reals
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