generic specification parameter elemdata using nat target sorts store; constants ∅ : store; functions . [ . ] : store × elem × data → store; # . : store → nat; . -- . : store × elem → store prio 9 left; predicates . ∈ . : elem × store; . ⊆ . : store × store; variables st : store; st0 : store; st1 : store; st2 : store; partial functions . [ . ] : store × elem → data with λ st, a. a ∈ st; induction store generated by ∅, [ ]; axioms Extension: st1 = st2 ↔ (∀ a. (a ∈ st1 ↔ a ∈ st2) ∧ st1[a] = st2[a]); used for: ls; In-empty: ¬ a ∈ ∅; used for: s, ls; In-insert: a ∈ st[b, d] ↔ a = b ∨ a ∈ st; used for: s, ls; At-same: st[a, d][a] = d; used for: s, ls; At-other: a ≠ b → st[b, d][a] = st[a]; used for: s, ls; Subset: st1 ⊆ st2 ↔ (∀ a. a ∈ st1 → a ∈ st2 ∧ st1[a] = st2[a]); used for: ls; Size-empty: # ∅ = 0; used for: s, ls; Size-insert: ¬ a ∈ st → # st[a, d] = # st + 1; used for: s, ls; Del-empty: ∅ -- a = ∅; used for: s, ls; Del-rec-same: st[a, d] -- a = st -- a; used for: s, ls; Del-rec-other: a ≠ b → st[b, d] -- a = (st -- a)[b, d]; end generic specification