intro f f_in
case mpr.intro.intro
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
Y : List Formula
Y_in : Y ∈ ress
w_LYRO : (M, w)⊨(L.diff Lcond ++ Y, R, O)
⊢ (M, w)⊨(L, R, O)
case mpr.intro.intro
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
Y : List Formula
Y_in : Y ∈ ress
w_LYRO : (M, w)⊨(L.diff Lcond ++ Y, R, O)
f : Formula
f_in : f ∈ L ∪ R ∪ (Option.map (Sum.elim negUnload negUnload) O).toList
⊢ evaluate M w f