Nuprl Lemma : rmin-max-cases

a,b:ℝ.  (a ≠  (((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: y real: all: x:A. B[x] implies:  Q or: P ∨ Q and: P ∧ Q
Definitions unfolded in proof :  all: x:A. B[x] implies:  Q rneq: x ≠ y or: P ∨ Q and: P ∧ Q cand: c∧ B uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a guard: {T} prop:
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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