Step
*
of Lemma
free-dist-lattice-property
No Annotations
∀T:Type. ∀eq:EqDecider(T). ∀L:BoundedDistributiveLattice. ∀eqL:EqDecider(Point(L)). ∀f:T ⟶ Point(L).
∃g:Hom(free-dist-lattice(T; eq);L). (f = (g o (λx.free-dl-inc(x))) ∈ (T ⟶ Point(L)))
BY
{ (Auto
THEN With
⌜λac.lattice-extend(L;eq;eqL;f;ac)⌝ (D 0)⋅
THEN Auto
THEN Try ((FunExt THEN RepUR ``compose`` 0 THEN Auto))) }
1
.....wf.....
1. T : Type@i'
2. eq : EqDecider(T)@i
3. L : BoundedDistributiveLattice@i'
4. eqL : EqDecider(Point(L))@i
5. f : T ⟶ Point(L)@i
⊢ λac.lattice-extend(L;eq;eqL;f;ac) ∈ Hom(free-dist-lattice(T; eq);L)
Latex:
Latex:
No Annotations
\mforall{}T:Type. \mforall{}eq:EqDecider(T). \mforall{}L:BoundedDistributiveLattice. \mforall{}eqL:EqDecider(Point(L)).
\mforall{}f:T {}\mrightarrow{} Point(L).
\mexists{}g:Hom(free-dist-lattice(T; eq);L). (f = (g o (\mlambda{}x.free-dl-inc(x))))
By
Latex:
(Auto
THEN With
\mkleeneopen{}\mlambda{}ac.lattice-extend(L;eq;eqL;f;ac)\mkleeneclose{} (D 0)\mcdot{}
THEN Auto
THEN Try ((FunExt THEN RepUR ``compose`` 0 THEN Auto)))
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