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Step * of Lemma lattice-extend-join

∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L:BoundedDistributiveLattice]. ∀[eqL:EqDecider(Point(L))]. ∀[f:T ⟶ Point(L)].
∀[a,b:Point(free-dist-lattice(T; eq))].
  lattice-extend(L;eq;eqL;f;a ∨ b) ≤ lattice-extend(L;eq;eqL;f;a) ∨ lattice-extend(L;eq;eqL;f;b)
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1. T : Type
2. eq : EqDecider(T)
3. L : BoundedDistributiveLattice
4. eqL : EqDecider(Point(L))
5. f : T ⟶ Point(L)
6. a : Point(free-dist-lattice(T; eq))
7. b : Point(free-dist-lattice(T; eq))
⊢ lattice-extend(L;eq;eqL;f;a ∨ b) ≤ lattice-extend(L;eq;eqL;f;a) ∨ lattice-extend(L;eq;eqL;f;b)

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Latex:

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Latex:
\mforall{}[T:Type].  \mforall{}[eq:EqDecider(T)].  \mforall{}[L:BoundedDistributiveLattice].  \mforall{}[eqL:EqDecider(Point(L))].
\mforall{}[f:T  {}\mrightarrow{}  Point(L)].  \mforall{}[a,b:Point(free-dist-lattice(T;  eq))].
    lattice-extend(L;eq;eqL;f;a  \mvee{}  b)  \mleq{}  lattice-extend(L;eq;eqL;f;a)  \mvee{}  lattice-extend(L;eq;eqL;f;b)


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