Documentation
Foundation
.
Propositional
.
Kripke2
.
AxiomHrd
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Imports
Init
Foundation.Propositional.Kripke2.Basic
Foundation.Vorspiel.Rel.Convergent
Foundation.Vorspiel.Rel.Coreflexive
Foundation.Vorspiel.Rel.Euclidean
Imported by
LO
.
Propositional
.
Kripke2
.
Model
.
IsHereditary
LO
.
Propositional
.
Kripke2
.
valid_axiomHrd_of_isHereditary
LO
.
Propositional
.
Kripke2
.
isHereditary_of_valid_axiomHrd
source
class
LO
.
Propositional
.
Kripke2
.
Model
.
IsHereditary
(
M
:
Model
)
:
Prop
hereditary
{
a
:
ℕ
}
{
x
y
:
M
.
World
}
:
M
.
Val
x
a
→
x
≺
y
→
M
.
Val
y
a
Instances
source
@[simp]
theorem
LO
.
Propositional
.
Kripke2
.
valid_axiomHrd_of_isHereditary
{
M
:
Model
}
{
a
:
ℕ
}
[
M
.
IsHereditary
]
:
M
⊧
Axioms.Hrd
#
a
source
theorem
LO
.
Propositional
.
Kripke2
.
isHereditary_of_valid_axiomHrd
{
M
:
Model
}
(
h
:
∀ (
a
:
ℕ
),
M
⊧
Axioms.Hrd
#
a
)
:
M
.
IsHereditary