### Nuprl Lemma : rmax_lb

`∀[x,y,z:ℝ].  uiff((x ≤ z) ∧ (y ≤ z);rmax(x;y) ≤ z)`

Proof

Definitions occuring in Statement :  rleq: `x ≤ y` rmax: `rmax(x;y)` real: `ℝ` uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` and: `P ∧ Q`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uiff: `uiff(P;Q)` and: `P ∧ Q` uimplies: `b supposing a` rleq: `x ≤ y` rnonneg: `rnonneg(x)` all: `∀x:A. B[x]` le: `A ≤ B` not: `¬A` implies: `P `` Q` false: `False` subtype_rel: `A ⊆r B` real: `ℝ` prop: `ℙ` guard: `{T}` rsub: `x - y` rev_uimplies: `rev_uimplies(P;Q)` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` cand: `A c∧ B`
Lemmas referenced :  less_than'_wf rsub_wf rmax_wf real_wf nat_plus_wf and_wf rleq_wf rleq-rmax rleq_transitivity rminus_wf rmin_wf req_weakening req_functionality req_transitivity rmin-req-rminus-rmax rminus_functionality rmax_functionality rminus-rminus radd_wf rnonneg_functionality radd_functionality radd-rmin rmin-nonneg
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut independent_pairFormation sqequalHypSubstitution productElimination thin sqequalRule lambdaEquality dependent_functionElimination hypothesisEquality independent_pairEquality because_Cache lemma_by_obid isectElimination applyEquality hypothesis setElimination rename minusEquality natural_numberEquality axiomEquality equalityTransitivity equalitySymmetry independent_isectElimination voidElimination isect_memberEquality independent_functionElimination

Latex:
\mforall{}[x,y,z:\mBbbR{}].    uiff((x  \mleq{}  z)  \mwedge{}  (y  \mleq{}  z);rmax(x;y)  \mleq{}  z)

Date html generated: 2016_05_18-AM-07_16_23
Last ObjectModification: 2015_12_28-AM-00_43_36

Theory : reals

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