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Step * 1 of Lemma lattice-meet-join-images-distrib

.....subterm..... T:t
2:n
1. L : BoundedDistributiveLattice@i'
2. eqL : EqDecider(Point(L))@i
3. as : fset(fset(Point(L)))@i
4. bs : fset(fset(Point(L)))@i
5. ∀[s1,s2:fset(Point(L))].  (\/(s1) ∧ \/(s2) = \/(f-union(eqL;eqL;s1;a.λb.a ∧ b"(s2))) ∈ Point(L))
⊢ f-union(eqL;eqL;λls./\(ls)"(as);a.λb.a ∧ b"(λls./\(ls)"(bs)))
= λls./\(ls)"(f-union(deq-fset(eqL);deq-fset(eqL);as;as.λbs.as ⋃ bs"(bs)))
∈ fset(Point(L))
BY
{ FsetExt }

1
1. L : BoundedDistributiveLattice@i'
2. eqL : EqDecider(Point(L))@i
3. as : fset(fset(Point(L)))@i
4. bs : fset(fset(Point(L)))@i
5. ∀[s1,s2:fset(Point(L))].  (\/(s1) ∧ \/(s2) = \/(f-union(eqL;eqL;s1;a.λb.a ∧ b"(s2))) ∈ Point(L))
6. a : Point(L)
7. a ∈ f-union(eqL;eqL;λls./\(ls)"(as);a.λb.a ∧ b"(λls./\(ls)"(bs)))
⊢ a ∈ λls./\(ls)"(f-union(deq-fset(eqL);deq-fset(eqL);as;as.λbs.as ⋃ bs"(bs)))

2
1. L : BoundedDistributiveLattice@i'
2. eqL : EqDecider(Point(L))@i
3. as : fset(fset(Point(L)))@i
4. bs : fset(fset(Point(L)))@i
5. ∀[s1,s2:fset(Point(L))].  (\/(s1) ∧ \/(s2) = \/(f-union(eqL;eqL;s1;a.λb.a ∧ b"(s2))) ∈ Point(L))
6. a : Point(L)
7. a ∈ λls./\(ls)"(f-union(deq-fset(eqL);deq-fset(eqL);as;as.λbs.as ⋃ bs"(bs)))
⊢ a ∈ f-union(eqL;eqL;λls./\(ls)"(as);a.λb.a ∧ b"(λls./\(ls)"(bs)))

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Latex:

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Latex:
.....subterm.....  T:t
2:n
1.  L  :  BoundedDistributiveLattice@i'
2.  eqL  :  EqDecider(Point(L))@i
3.  as  :  fset(fset(Point(L)))@i
4.  bs  :  fset(fset(Point(L)))@i
5.  \mforall{}[s1,s2:fset(Point(L))].    (\mbackslash{}/(s1)  \mwedge{}  \mbackslash{}/(s2)  =  \mbackslash{}/(f-union(eqL;eqL;s1;a.\mlambda{}b.a  \mwedge{}  b"(s2))))
\mvdash{}  f-union(eqL;eqL;\mlambda{}ls./\mbackslash{}(ls)"(as);a.\mlambda{}b.a  \mwedge{}  b"(\mlambda{}ls./\mbackslash{}(ls)"(bs)))
=  \mlambda{}ls./\mbackslash{}(ls)"(f-union(deq-fset(eqL);deq-fset(eqL);as;as.\mlambda{}bs.as  \mcup{}  bs"(bs)))


By

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Latex:
FsetExt

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