mathlib3 documentation

order.prop_instances

The order on Prop #

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Instances on Prop such as distrib_lattice, bounded_order, linear_order.

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Propositions form a distributive lattice.

Equations
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Propositions form a bounded order.

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noncomputable def Prop.linear_order  :
Equations
@[simp]
theorem sup_Prop_eq  :
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theorem pi.disjoint_iff {ι : Type u_1} {α' : ι Type u_2} [Π (i : ι), partial_order (α' i)] [Π (i : ι), order_bot (α' i)] {f g : Π (i : ι), α' i} :
disjoint f g (i : ι), disjoint (f i) (g i)
theorem pi.codisjoint_iff {ι : Type u_1} {α' : ι Type u_2} [Π (i : ι), partial_order (α' i)] [Π (i : ι), order_top (α' i)] {f g : Π (i : ι), α' i} :
codisjoint f g (i : ι), codisjoint (f i) (g i)
theorem pi.is_compl_iff {ι : Type u_1} {α' : ι Type u_2} [Π (i : ι), partial_order (α' i)] [Π (i : ι), bounded_order (α' i)] {f g : Π (i : ι), α' i} :
is_compl f g (i : ι), is_compl (f i) (g i)
@[simp]
theorem Prop.disjoint_iff {P Q : Prop} :
disjoint P Q ¬(P Q)
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theorem Prop.codisjoint_iff {P Q : Prop} :
@[simp]
theorem Prop.is_compl_iff {P Q : Prop} :
is_compl P Q ¬(P Q)