Nuprl Lemma : sp-join-com
∀[x,y:Sierpinski].  (x ∨ y = y ∨ x ∈ Sierpinski)
Proof
Definitions occuring in Statement : 
sp-join: f ∨ g
, 
Sierpinski: Sierpinski
, 
uall: ∀[x:A]. B[x]
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
iff: P 
⇐⇒ Q
, 
implies: P 
⇒ Q
, 
rev_implies: P 
⇐ Q
, 
cand: A c∧ B
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
Sierpinski-equal, 
sp-join_wf, 
sp-join-is-bottom, 
equal_wf, 
Sierpinski_wf, 
Sierpinski-bottom_wf, 
subtype-Sierpinski
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
productElimination, 
independent_isectElimination, 
independent_pairFormation, 
lambdaFormation, 
independent_functionElimination, 
applyEquality, 
sqequalRule, 
because_Cache, 
isect_memberEquality, 
axiomEquality
Latex:
\mforall{}[x,y:Sierpinski].    (x  \mvee{}  y  =  y  \mvee{}  x)
Date html generated:
2019_10_31-AM-06_36_33
Last ObjectModification:
2015_12_28-AM-11_21_00
Theory : synthetic!topology
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