Nuprl Lemma : rmin-rmax-distrib-strong
∀a,b,c:ℝ. (rmin(a;rmax(b;c)) = rmax(rmin(a;b);rmin(a;c)) ∈ ℝ)
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
rmax: rmax(x;y),
real: ℝ,
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
rmin: rmin(x;y),
rmax: rmax(x;y),
squash: ↓T,
prop: ℙ,
real: ℝ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
implies-equal-real,
rmin_wf,
rmax_wf,
equal_wf,
squash_wf,
true_wf,
imin_wf,
imax_wf,
imax-imin-distributive,
iff_weakening_equal,
nat_plus_wf,
real_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
sqequalRule,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
intEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination
Latex:
\mforall{}a,b,c:\mBbbR{}. (rmin(a;rmax(b;c)) = rmax(rmin(a;b);rmin(a;c)))
Date html generated:
2017_10_03-AM-08_22_43
Last ObjectModification:
2017_07_28-AM-07_22_31
Theory : reals
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