Nuprl Lemma : rmin-com
∀[x,y:ℝ]. (rmin(x;y) = rmin(y;x))
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_com,
imin_wf,
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:\mBbbR{}]. (rmin(x;y) = rmin(y;x))
Date html generated:
2017_10_03-AM-08_22_24
Last ObjectModification:
2017_07_28-AM-07_22_18
Theory : reals
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