constructor
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F ↔ fastAdmitsAux v u ∅ F
case mp
F : Formula
v u : VarName
⊢ admitsAux v u ∅ F → fastAdmitsAux v u ∅ F

case mpr
F : Formula
v u : VarName
⊢ fastAdmitsAux v u ∅ F → admitsAux v u ∅ F