Nuprl Lemma : rmin-assoc
∀[x,y,z:ℝ].  (rmin(rmin(x;y);z) = rmin(x;rmin(y;z)))
Proof
Definitions occuring in Statement : 
rmin: rmin(x;y)
, 
req: x = y
, 
real: ℝ
, 
uall: ∀[x:A]. B[x]
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
real: ℝ
, 
squash: ↓T
, 
rmin: rmin(x;y)
, 
prop: ℙ
, 
true: True
, 
subtype_rel: A ⊆r B
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
rev_implies: P 
⇐ Q
, 
implies: P 
⇒ Q
Lemmas referenced : 
req_weakening, 
rmin_wf, 
equal_wf, 
squash_wf, 
true_wf, 
imin_wf, 
imin_assoc, 
iff_weakening_equal, 
nat_plus_wf, 
regular-int-seq_wf, 
req_witness, 
real_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
independent_isectElimination, 
because_Cache, 
applyLambdaEquality, 
setElimination, 
rename, 
sqequalRule, 
imageMemberEquality, 
baseClosed, 
imageElimination, 
dependent_set_memberEquality, 
functionExtensionality, 
applyEquality, 
lambdaEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality, 
intEquality, 
natural_numberEquality, 
productElimination, 
independent_functionElimination, 
isect_memberEquality
Latex:
\mforall{}[x,y,z:\mBbbR{}].    (rmin(rmin(x;y);z)  =  rmin(x;rmin(y;z)))
Date html generated:
2017_10_03-AM-08_22_29
Last ObjectModification:
2017_07_28-AM-07_22_22
Theory : reals
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