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Proof step 12 from proof keyset-overwrite-add (previous step)

keyset(kar[n, ki], m0) ++ kar[n] = keyset(kar, m0) ++ ki, n < m0, m0 < # kar, n < # kar, n + 1 < # kar ⊦ keyset(kar[n, ki], m0) ++ kar[m0] ++ kar[n] = keyset(kar, m0) ++ kar[m0] ++ ki, m0 = n

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: set-basic, inst: keyindex-set name: sw seq: ⊦ s ++ ki ++ ki0 = s ++ ki0 ++ ki subst: [ki0, ki, s] → [kar[n], kar[m0], keyset(kar[n, ki], m0)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ s ++ ki ++ ki0 = s ++ ki0 ++ ki ↔ true; (s) Used terms: kar[n], kar[m0], keyset(kar[n, ki], m0)