stackInSomeState : {l m : Level } {D : Set l} {t : Set m } (s : SingleLinkedStack D ) @$\rightarrow$@ Stack {l} {m} D {t}  ( SingleLinkedStack  D )
stackInSomeState s =  record { stack = s ; stackMethods = singleLinkedStackSpec }

push@$\rightarrow$@push@$\rightarrow$@pop2 : {l : Level } {D : Set l} (x y : D ) (s : SingleLinkedStack D ) @$\rightarrow$@ pushStack (stackInSomeState s)  x (\s1 @$\rightarrow$@ pushStack s1 y (\s2 @$\rightarrow$@ pop2Stack s2 (\s3 y1 x1 @$\rightarrow$@
   (Just x @$\equiv$@ x1) ∧ (Just y @$\equiv$@ y1))))
push@$\rightarrow$@push@$\rightarrow$@pop2 {l} {D} x y s = record { pi1 = refl ; pi2 = refl }