### 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

Home Index