Nuprl Lemma : rmin-rmax-distrib
∀a,b,c:ℝ. (rmin(a;rmax(b;c)) = rmax(rmin(a;b);rmin(a;c)))
Proof
Definitions occuring in Statement :
rmin: rmin(x;y),
rmax: rmax(x;y),
req: x = y,
real: ℝ,
all: ∀x:A. B[x]
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
squash: ↓T,
uall: ∀[x:A]. B[x],
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
real_wf,
req_weakening,
iff_weakening_equal,
rmin_wf,
rmax_wf,
rmin-rmax-distrib-strong,
true_wf,
squash_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
dependent_functionElimination,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}a,b,c:\mBbbR{}. (rmin(a;rmax(b;c)) = rmax(rmin(a;b);rmin(a;c)))
Date html generated:
2016_05_18-AM-06_59_43
Last ObjectModification:
2016_01_13-PM-04_23_34
Theory : reals
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