[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 32 from proof insert-correct (previous step)

⟨loop if ¬ found? then {if T3[h1(a)] = empty then {T3 := T3[h1(a), full(a)]; found? := true}; if ¬ found? then {a := T3[h1(a)].elem, T3 := T3[h1(a), T3[h1(a)].elem:= a]; if T2[h2(a)] = empty then {T2 := T2[h2(a), full(a)]; found? := true}}; if ¬ found? then a := T2[h2(a)].elem, T2 := T2[h2(a), T2[h2(a)].elem:= a]} times m⟩ (T3 = T ∧ found? ∧ a = a1 ∧ T2 = T0), ∀ kappa0, found?0, T1, h1, a, T2, h2, T, a1, T0. kappa0 < m + 1 → ⟨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 kappa0⟩ (T1 = T ∧ found?0 ∧ a = a1 ∧ T2 = T0) ∧ ¬ found?0 ∧ T2[h2(a)] ≠ full(a) ∧ T1[h1(a)] ≠ full(a) ∧ disj(T1, T2) ∧ inv(T2, h2) ∧ inv(T1, h1) ∧ (abs(T1, T2, h1, h2) ++ a ≠ abs(T, T0, h1, h2) ∨ ¬ inv(T, h1) ∨ ¬ inv(T0, h2) ∨ ¬ disj(T, T0)) → false, found?, T3 = T1[h1(a), full(a)], T1[h1(a)] = empty, T2[h2(a)] ≠ full(a), 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 loop exit applied rule loop exit left

And obtained the following new goals

Proof step 31:
∀ kappa0, found?0, T1, h1, a, T2, h2, T, a1, T0. kappa0 < m + 1 → ⟨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 kappa0⟩ (T1 = T ∧ found?0 ∧ a = a1 ∧ T2 = T0) ∧ ¬ found?0 ∧ T2[h2(a)] ≠ full(a) ∧ T1[h1(a)] ≠ full(a) ∧ disj(T1, T2) ∧ inv(T2, h2) ∧ inv(T1, h1) ∧ (abs(T1, T2, h1, h2) ++ a ≠ abs(T, T0, h1, h2) ∨ ¬ inv(T, h1) ∨ ¬ inv(T0, h2) ∨ ¬ disj(T, T0)) → false, found?, T3 = T1[h1(a), full(a)], T1[h1(a)] = empty, T2[h2(a)] ≠ full(a), 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?, a = a1, T2 = T0 ⊦

Rule argument

Additional information

[Concretesimprules(())]