Nuprl Lemma : rmin-rleq
∀[x,y:ℝ].  ((rmin(x;y) ≤ x) ∧ (rmin(x;y) ≤ y))
Proof
Definitions occuring in Statement : 
rleq: x ≤ y
, 
rmin: rmin(x;y)
, 
real: ℝ
, 
uall: ∀[x:A]. B[x]
, 
and: P ∧ Q
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
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
, 
uimplies: b supposing a
, 
rge: x ≥ y
, 
uiff: uiff(P;Q)
, 
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced : 
less_than'_wf, 
rsub_wf, 
rmin_wf, 
real_wf, 
nat_plus_wf, 
rminus_wf, 
rmax_wf, 
rminus_functionality_wrt_rleq, 
rleq-rmax, 
rleq_functionality, 
rmin-req-rminus-rmax, 
req_weakening, 
req_inversion, 
rminus-rminus
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
independent_pairFormation, 
hypothesis, 
sqequalRule, 
sqequalHypSubstitution, 
productElimination, 
thin, 
independent_pairEquality, 
lambdaEquality, 
dependent_functionElimination, 
hypothesisEquality, 
because_Cache, 
lemma_by_obid, 
isectElimination, 
applyEquality, 
setElimination, 
rename, 
minusEquality, 
natural_numberEquality, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
isect_memberEquality, 
voidElimination, 
independent_isectElimination
Latex:
\mforall{}[x,y:\mBbbR{}].    ((rmin(x;y)  \mleq{}  x)  \mwedge{}  (rmin(x;y)  \mleq{}  y))
Date html generated:
2016_05_18-AM-07_16_35
Last ObjectModification:
2015_12_28-AM-00_43_19
Theory : reals
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