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Proof step 10 from proof keyset-overwrite-add (previous step)

n < m0, m0 < # kar, n < # kar, n + 1 < # kar, ∀ n, kar, ki. n < m0 ∧ n < # kar ∧ m0 ≤ # kar → keyset(kar[n, ki], m0) ++ kar[n] = keyset(kar, m0) ++ ki ⊦ keyset(kar[n, ki], m0) ++ kar[m0] ++ kar[n] = keyset(kar, m0) ++ kar[m0] ++ ki, m0 = n

User applied rule all left

And obtained the following new goals

Proof step 11:
n + 1 < # kar, n < # kar, m0 < # kar, n < m0, n < m0 ∧ n < # kar ∧ m0 ≤ # kar → keyset(kar[n, ki], m0) ++ kar[n] = keyset(kar, m0) ++ ki ⊦ keyset(kar[n, ki], m0) ++ kar[m0] ++ kar[n] = keyset(kar, m0) ++ kar[m0] ++ ki, m0 = n

Rule argument

pos: left 5 terms: n, kar, ki abort: F discard: T computed: F

Additional information

Used terms: n, kar, ki