---

Step * 1 1 1 1 of Lemma lattice-axioms-iff-order


1. l : LatticeStructure@i'
2. lattice-axioms(l)@i
3. λ2a b.a ≤ b ∈ Point(l) ⟶ Point(l) ⟶ ℙ
⊢ ((∀[a,b:Point(l)].  least-upper-bound(Point(l);x,y.x ≤ y;a;b;a ∨ b))
∧ (∀[a,b:Point(l)].  greatest-lower-bound(Point(l);x,y.x ≤ y;a;b;a ∧ b)))
∧ Order(Point(l);x,y.x ≤ y)
BY
{ Auto }

---

Latex:

---

Latex:

1.  l  :  LatticeStructure@i'
2.  lattice-axioms(l)@i
3.  \mlambda{}\msubtwo{}a  b.a  \mleq{}  b  \mmember{}  Point(l)  {}\mrightarrow{}  Point(l)  {}\mrightarrow{}  \mBbbP{}
\mvdash{}  ((\mforall{}[a,b:Point(l)].    least-upper-bound(Point(l);x,y.x  \mleq{}  y;a;b;a  \mvee{}  b))
\mwedge{}  (\mforall{}[a,b:Point(l)].    greatest-lower-bound(Point(l);x,y.x  \mleq{}  y;a;b;a  \mwedge{}  b)))
\mwedge{}  Order(Point(l);x,y.x  \mleq{}  y)


By

---

Latex:
Auto

---

Home Index