Nuprl Lemma : dM-point
∀[I:Top]
(Point(dM(I)) ~ {ac:fset(fset(names(I) + names(I)))|
↑fset-antichain(union-deq(names(I);names(I);NamesDeq;NamesDeq);ac)} )
Proof
Definitions occuring in Statement :
dM: dM(I),
names-deq: NamesDeq,
names: names(I),
lattice-point: Point(l),
fset-antichain: fset-antichain(eq;ac),
fset: fset(T),
union-deq: union-deq(A;B;a;b),
assert: ↑b,
uall: ∀[x:A]. B[x],
top: Top,
set: {x:A| B[x]} ,
union: left + right,
sqequal: s ~ t
Definitions unfolded in proof :
dM: dM(I),
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
free-DeMorgan-lattice: free-DeMorgan-lattice(T;eq)
Lemmas referenced :
free-dma-point,
free-dl-point,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
introduction,
sqequalAxiom
Latex:
\mforall{}[I:Top]
(Point(dM(I)) \msim{} \{ac:fset(fset(names(I) + names(I)))|
\muparrow{}fset-antichain(union-deq(names(I);names(I);NamesDeq;NamesDeq);ac)\} )
Date html generated:
2016_05_18-AM-11_56_23
Last ObjectModification:
2015_12_28-PM-03_08_49
Theory : cubical!type!theory
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