Nuprl Lemma : free-dlwc-meet
∀[T,eq,a,b,cs:Top]. (a ∧ b ~ glb(λs.fset-contains-none(eq;s;x.cs[x]);a;b))
Proof
Definitions occuring in Statement :
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-meet: a ∧ b,
fset-constrained-ac-glb: glb(P;ac1;ac2),
fset-contains-none: fset-contains-none(eq;s;x.Cs[x]),
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
lambda: λx.A[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
free-dist-lattice-with-constraints: free-dist-lattice-with-constraints(T;eq;x.Cs[x]),
lattice-meet: a ∧ b,
constrained-antichain-lattice: constrained-antichain-lattice(T;eq;P),
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,cs:Top]. (a \mwedge{} b \msim{} glb(\mlambda{}s.fset-contains-none(eq;s;x.cs[x]);a;b))
Date html generated:
2020_05_20-AM-08_48_28
Last ObjectModification:
2015_12_28-PM-01_58_48
Theory : lattices
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