Nuprl Lemma : qmax-symmetry
∀[x,y:ℚ].  (qmax(x;y) = qmax(y;x) ∈ ℚ)
Proof
Definitions occuring in Statement : 
qmax: qmax(x;y)
, 
rationals: ℚ
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
qmax: qmax(x;y)
, 
guard: {T}
, 
uimplies: b supposing a
, 
true: True
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
ifthenelse: if b then t else f fi 
, 
bfalse: ff
, 
squash: ↓T
, 
prop: ℙ
, 
false: False
Lemmas referenced : 
q_le_wf, 
bool_wf, 
equal-wf-T-base, 
assert_wf, 
qle_wf, 
qle_antisymmetry, 
bnot_wf, 
not_wf, 
uiff_transitivity2, 
eqtt_to_assert, 
assert-q_le-eq, 
uiff_transitivity, 
eqff_to_assert, 
assert_of_bnot, 
squash_wf, 
true_wf, 
equal_wf, 
qle_complement_qorder, 
qless_transitivity, 
qless_irreflexivity
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
hypothesis, 
because_Cache, 
sqequalRule, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
thin, 
hypothesisEquality, 
axiomEquality, 
extract_by_obid, 
equalityTransitivity, 
equalitySymmetry, 
baseClosed, 
independent_isectElimination, 
natural_numberEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
independent_functionElimination, 
productElimination, 
applyEquality, 
lambdaEquality, 
imageElimination, 
universeEquality, 
imageMemberEquality, 
dependent_functionElimination, 
voidElimination
Latex:
\mforall{}[x,y:\mBbbQ{}].    (qmax(x;y)  =  qmax(y;x))
Date html generated:
2018_05_21-PM-11_57_22
Last ObjectModification:
2017_07_26-PM-06_47_33
Theory : rationals
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