have IHα := localDiamondTruth α (⌈β⌉ψ) W M w
ψ : Formula
W : Type
M : KripkeModel W
w : W
α β : Program
⊢ evaluate M w (~⌈α⌉⌈β⌉ψ) ↔ evaluate M w (dis (List.map (fun Fδ => Con (Yset Fδ ψ)) (H (α;'β))))
ψ : Formula
W : Type
M : KripkeModel W
w : W
α β : Program
IHα : evaluate M w (~⌈α⌉⌈β⌉ψ) ↔ evaluate M w (dis (List.map (fun Fδ => Con (Yset Fδ (⌈β⌉ψ))) (H α)))
⊢ evaluate M w (~⌈α⌉⌈β⌉ψ) ↔ evaluate M w (dis (List.map (fun Fδ => Con (Yset Fδ ψ)) (H (α;'β))))