Nuprl Lemma : rmax_functionality_wrt_rleq
∀[x1,x2,y1,y2:ℝ]. (rmax(x1;y1) ≤ rmax(x2;y2)) supposing ((y1 ≤ y2) and (x1 ≤ x2))
Proof
Definitions occuring in Statement :
rleq: x ≤ y,
rmax: rmax(x;y),
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
cand: A c∧ B,
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}
Lemmas referenced :
rmax_lb,
rmax_wf,
less_than'_wf,
rsub_wf,
real_wf,
nat_plus_wf,
rleq_wf,
rleq-rmax,
rleq_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
independent_pairFormation,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
independent_pairEquality,
because_Cache,
applyEquality,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination
Latex:
\mforall{}[x1,x2,y1,y2:\mBbbR{}]. (rmax(x1;y1) \mleq{} rmax(x2;y2)) supposing ((y1 \mleq{} y2) and (x1 \mleq{} x2))
Date html generated:
2016_05_18-AM-07_16_30
Last ObjectModification:
2015_12_28-AM-00_43_25
Theory : reals
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