Step
*
2
of Lemma
face-lattice-basis
1. T : Type
2. eq : EqDecider(T)
3. x : fset(fset(T + T))
4. ↑fset-antichain(union-deq(T;T;eq;eq);x)
5. fset-all(x;a.fset-contains-none(union-deq(T;T;eq;eq);a;x.face-lattice-constraints(x)))
6. s : fset(T + T)
7. u : T + T
8. ¬↑fset-null({c ∈ face-lattice-constraints(u) | deq-f-subset(union-deq(T;T;eq;eq)) c {u}})
⊢ {{u}}
= {}
∈ {ac:fset(fset(T + T))|
(↑fset-antichain(union-deq(T;T;eq;eq);ac))
∧ fset-all(ac;a.fset-contains-none(union-deq(T;T;eq;eq);a;x.face-lattice-constraints(x)))}
BY
{ D -1 }
1
1. T : Type
2. eq : EqDecider(T)
3. x : fset(fset(T + T))
4. ↑fset-antichain(union-deq(T;T;eq;eq);x)
5. fset-all(x;a.fset-contains-none(union-deq(T;T;eq;eq);a;x.face-lattice-constraints(x)))
6. s : fset(T + T)
7. u : T + T
⊢ ↑fset-null({c ∈ face-lattice-constraints(u) | deq-f-subset(union-deq(T;T;eq;eq)) c {u}})
Latex:
Latex:
1. T : Type
2. eq : EqDecider(T)
3. x : fset(fset(T + T))
4. \muparrow{}fset-antichain(union-deq(T;T;eq;eq);x)
5. fset-all(x;a.fset-contains-none(union-deq(T;T;eq;eq);a;x.face-lattice-constraints(x)))
6. s : fset(T + T)
7. u : T + T
8. \mneg{}\muparrow{}fset-null(\{c \mmember{} face-lattice-constraints(u) | deq-f-subset(union-deq(T;T;eq;eq)) c \{u\}\})
\mvdash{} \{\{u\}\} = \{\}
By
Latex:
D -1
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