Step
*
1
1
2
2
of Lemma
free-DeMorgan-algebra-property
1. T : Type@i'
2. eq : EqDecider(T)@i
3. dm : DeMorganAlgebra@i'
4. eq2 : EqDecider(Point(dm))@i
5. f : T ⟶ Point(dm)@i
6. g : Hom(free-DeMorgan-lattice(T;eq);dm)
7. (λp.case p of inl(a) => f a | inr(a) => ¬(f a)) = (g o (λx.free-dl-inc(x))) ∈ ((T + T) ⟶ Point(dm))
8. ∀i:T. ((g <i>) = (f i) ∈ Point(dm))
9. ∀i:T. ((g <1-i>) = ¬(f i) ∈ Point(dm))
10. ∀[a:Point(free-DeMorgan-algebra(T;eq))]. ((g a) = ¬(g ¬(a)) ∈ Point(dm))
⊢ ∀[a:Point(free-DeMorgan-algebra(T;eq))]. (¬(g a) = (g ¬(a)) ∈ Point(dm))
BY
{ ((D 0 THENA Auto) THEN RWO "-2" 0 THEN Auto) }
Latex:
Latex:
1. T : Type@i'
2. eq : EqDecider(T)@i
3. dm : DeMorganAlgebra@i'
4. eq2 : EqDecider(Point(dm))@i
5. f : T {}\mrightarrow{} Point(dm)@i
6. g : Hom(free-DeMorgan-lattice(T;eq);dm)
7. (\mlambda{}p.case p of inl(a) => f a | inr(a) => \mneg{}(f a)) = (g o (\mlambda{}x.free-dl-inc(x)))
8. \mforall{}i:T. ((g <i>) = (f i))
9. \mforall{}i:T. ((g ə-i>) = \mneg{}(f i))
10. \mforall{}[a:Point(free-DeMorgan-algebra(T;eq))]. ((g a) = \mneg{}(g \mneg{}(a)))
\mvdash{} \mforall{}[a:Point(free-DeMorgan-algebra(T;eq))]. (\mneg{}(g a) = (g \mneg{}(a)))
By
Latex:
((D 0 THENA Auto) THEN RWO "-2" 0 THEN Auto)
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