[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 208 from proof insert-correct (previous step)

⟨loop if ¬ found?0 then {if T1[h1(a)] = empty then {T1 := T1[h1(a), full(a)]; found?0 := true}; if ¬ found?0 then {a := T1[h1(a)].elem, T1 := T1[h1(a), T1[h1(a)].elem:= a]; if T2[h2(a)] = empty then {T2 := T2[h2(a), full(a)]; found?0 := true}}; if ¬ found?0 then a := T2[h2(a)].elem, T2 := T2[h2(a), T2[h2(a)].elem:= a]} times kappa⟩ ((T1 = T ∧ (found?0 ↔ found?1) ∧ a = a0 ∧ T2 = T0) ∧ ¬ ¬ found?0), ⟨lookup(a, T1, T2, h1, h2; found?)⟩ (found? ↔ found?0), inv(T1, h1), inv(T2, h2), disj(T1, T2), abs(T1, T2, h1, h2) ++ a ≠ abs(T, T0, h1, h2) ∨ ¬ inv(T, h1) ∨ ¬ inv(T0, h2) ∨ ¬ disj(T, T0) ⊦

Heuristic split applied rule split left

And obtained the following new goals

Proof step 207:
⟨loop if ¬ found?0 then {if T1[h1(a)] = empty then {T1 := T1[h1(a), full(a)]; found?0 := true}; if ¬ found?0 then {a := T1[h1(a)].elem, T1 := T1[h1(a), T1[h1(a)].elem:= a]; if T2[h2(a)] = empty then {T2 := T2[h2(a), full(a)]; found?0 := true}}; if ¬ found?0 then a := T2[h2(a)].elem, T2 := T2[h2(a), T2[h2(a)].elem:= a]} times kappa⟩ (T1 = T3 ∧ (found?0 ↔ found?2) ∧ a = a1 ∧ T2 = T4), ⟨lookup(a, T1, T2, h1, h2; found?)⟩ (found? ↔ found?0), inv(T1, h1), inv(T2, h2), disj(T1, T2), abs(T1, T2, h1, h2) ++ a ≠ abs(T, T0, h1, h2) ∨ ¬ inv(T, h1) ∨ ¬ inv(T0, h2) ∨ ¬ disj(T, T0), T3 = T, found?2 ↔ found?1, a1 = a0, T4 = T0, ¬ ¬ found?2 ⊦

Rule argument

pos:left 1

Additional information

[Concretesimprules(())]