Nuprl Lemma : free-dl-join
∀[T,eq,a,b:Top]. (a ∨ b ~ fset-ac-lub(eq;a;b))
Proof
Definitions occuring in Statement :
free-dist-lattice: free-dist-lattice(T; eq),
lattice-join: a ∨ b,
fset-ac-lub: fset-ac-lub(eq;ac1;ac2),
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dist-lattice: free-dist-lattice(T; eq),
lattice-join: a ∨ b,
mk-bounded-distributive-lattice: mk-bounded-distributive-lattice,
mk-bounded-lattice: mk-bounded-lattice(T;m;j;z;o),
all: ∀x:A. B[x],
top: Top,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt
Lemmas referenced :
rec_select_update_lemma,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
axiomSqEquality,
isectElimination,
hypothesisEquality,
because_Cache
Latex:
\mforall{}[T,eq,a,b:Top]. (a \mvee{} b \msim{} fset-ac-lub(eq;a;b))
Date html generated:
2020_05_20-AM-08_45_14
Last ObjectModification:
2015_12_28-PM-01_59_58
Theory : lattices
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