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Proof step 215 from proof insert-correct (previous step)

⟨insert(a, h1, h2; T1, T2)⟩ (T1 = T ∧ T2 = T0), 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) ⊦

User applied rule call left

And obtained the following new goals

Proof step 214:
⟨let found? = false in {lookup(a, T1, T2, h1, h2; found?); T4 := T2, T3 := T1; while ¬ found? do {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 T4[h2(a)] = empty then {T4 := T4[h2(a), full(a)]; found? := true}}; if ¬ found? then a := T4[h2(a)].elem, T4 := T4[h2(a), T4[h2(a)].elem:= a]}}⟩ (T3 = T ∧ T4 = T0), 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) ⊦

Rule argument

pos:left 1

Additional information

[Concretesimprules((Csimpdecl(insert(a, h1, h2; T1, T2) {let found? = false in {lookup(a, T1, T2, h1, h2; found?); while ¬ found? do {if T1[h1(a)] = empty then {T1 := T1[h1(a), full(a)]; found? := true}; if ¬ found? 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? := true}}; if ¬ found? then a := T2[h2(a)].elem, T2 := T2 [h2(a), T2[h2(a)].elem:= a ]}} })))]