Nuprl Lemma : Sierpinski-equal2
∀[x,y:Sierpinski].  uiff(x = y ∈ Sierpinski;x = ⊤ ∈ Sierpinski 
⇐⇒ y = ⊤ ∈ Sierpinski)
Proof
Definitions occuring in Statement : 
Sierpinski: Sierpinski
, 
Sierpinski-top: ⊤
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
iff: P 
⇐⇒ Q
, 
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
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
, 
not: ¬A
, 
false: False
Lemmas referenced : 
equal-wf-T-base, 
Sierpinski_wf, 
equal_wf, 
Sierpinski-equal, 
not-Sierpinski-top, 
Sierpinski-unequal, 
iff_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
independent_pairFormation, 
lambdaFormation, 
equalityTransitivity, 
equalitySymmetry, 
hypothesis, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
baseClosed, 
because_Cache, 
sqequalRule, 
productElimination, 
independent_pairEquality, 
lambdaEquality, 
dependent_functionElimination, 
axiomEquality, 
independent_isectElimination, 
independent_functionElimination, 
voidElimination, 
isect_memberEquality
Latex:
\mforall{}[x,y:Sierpinski].    uiff(x  =  y;x  =  \mtop{}  \mLeftarrow{}{}\mRightarrow{}  y  =  \mtop{})
Date html generated:
2019_10_31-AM-06_36_29
Last ObjectModification:
2017_07_28-AM-09_12_15
Theory : synthetic!topology
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