simp only [List.mem_union_iff, List.mem_append]
case h.right.inl.inr
W : Type
L R : List Formula
O : Option (NegLoadFormula ⊕ NegLoadFormula)
M : KripkeModel W
w : W
Lcond : List Formula
ress : List (List Formula)
orule : OneSidedLocalRule Lcond ress
osTruth : evaluate M w (Con Lcond) ↔ evaluate M w (discon ress)
preconditionProof : Lcond.Sublist L
w_LRO : (M, w)⊨(L, R, O)
Y : List Formula
Y_in : Y ∈ ress
claim : ∀ f ∈ Y, evaluate M w f
f : Formula
f_in_R : f ∈ R
⊢ f ∈ L ∪ R ∪ (Option.map (Sum.elim negUnload negUnload) O).toList
case h.right.inl.inr
W : Type
L R : List Formula
O : Option (NegLoadFormula ⊕ NegLoadFormula)
M : KripkeModel W
w : W
Lcond : List Formula
ress : List (List Formula)
orule : OneSidedLocalRule Lcond ress
osTruth : evaluate M w (Con Lcond) ↔ evaluate M w (discon ress)
preconditionProof : Lcond.Sublist L
w_LRO : (M, w)⊨(L, R, O)
Y : List Formula
Y_in : Y ∈ ress
claim : ∀ f ∈ Y, evaluate M w f
f : Formula
f_in_R : f ∈ R
⊢ (f ∈ L ∨ f ∈ R) ∨ f ∈ (Option.map (Sum.elim negUnload negUnload) O).toList