def
LO.System.imply_boxdot_boxdot_of_imply_boxdot_plain
{S : Type u_1}
{F : Type u_2}
[BasicModalLogicalConnective F]
[DecidableEq F]
[System F S]
{𝓢 : S}
[System.GL 𝓢]
{φ ψ : F}
(h : 𝓢 ⊢ ⊡φ ➝ ψ)
:
Equations
- One or more equations did not get rendered due to their size.
Instances For
theorem
LO.System.imply_boxdot_boxdot_of_imply_boxdot_plain!
{S : Type u_1}
{F : Type u_2}
[BasicModalLogicalConnective F]
[DecidableEq F]
[System F S]
{𝓢 : S}
[System.GL 𝓢]
{φ ψ : F}
(h : 𝓢 ⊢! ⊡φ ➝ ψ)
:
def
LO.System.imply_boxdot_axiomT_of_imply_boxdot_boxdot
{S : Type u_1}
{F : Type u_2}
[BasicModalLogicalConnective F]
[DecidableEq F]
[System F S]
{𝓢 : S}
[System.GL 𝓢]
{φ ψ : F}
(h : 𝓢 ⊢ ⊡φ ➝ ⊡ψ)
:
Equations
- One or more equations did not get rendered due to their size.
Instances For
def
LO.System.imply_box_box_of_imply_boxdot_axiomT
{S : Type u_1}
{F : Type u_2}
[BasicModalLogicalConnective F]
[DecidableEq F]
[System F S]
{𝓢 : S}
[System.GL 𝓢]
{φ ψ : F}
(h : 𝓢 ⊢ ⊡φ ➝ □ψ ➝ ψ)
:
Equations
Instances For
theorem
LO.System.imply_box_box_of_imply_boxdot_plain!
{S : Type u_1}
{F : Type u_2}
[BasicModalLogicalConnective F]
[DecidableEq F]
[System F S]
{𝓢 : S}
[System.GL 𝓢]
{φ ψ : F}
(h : 𝓢 ⊢! ⊡φ ➝ ψ)
:
theorem
LO.Modal.Hilbert.GL.unnecessitation!
{φ : Formula ℕ}
:
Hilbert.GL ℕ ⊢! □φ → Hilbert.GL ℕ ⊢! φ
Equations
- LO.Modal.Hilbert.GL.instUnnecessitationNatFormula = { unnec := fun {φ : LO.Modal.Formula ℕ} (h : LO.Modal.Hilbert.GL ℕ ⊢ □φ) => Nonempty.some ⋯ }