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Proof step 15 from proof keyset-xchg (previous step)

n1 + 1 < # kar, n1 < # kar, n0 < # kar, n1 < n0, ∀ n1, n, kar. n1 < n0 ∧ n < n0 ∧ n1 < # kar ∧ n < # kar ∧ n0 ≤ # kar → keyset(kar[n, kar[n1]][n1, kar[n]], n0) = keyset(kar, n0) ⊦ keyset(kar[n0, kar[n1]][n1, kar[n0]], n0) ++ kar[n1] = keyset(kar, n0) ++ kar[n0], n0 = n1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
m ≠ n ⊦ kar[m, ki][n, ki0] = kar[n, ki0][m, ki]

Rule argument

spec: array, inst: key-index-array name: cputput-reverse seq: m ≠ n ⊦ kar[m, ki][n, ki0] = kar[n, ki0][m, ki] subst: [ki0, n, ki, m, kar] → [kar[n0], n1, kar[n1], n0, kar] flags: <all paths>

Additional information

Used simplifier rules: key-set-write-other: m ≤ n, n < # kar ⊦ keyset(kar[n, ki], m) = keyset(kar, m);%keyset-overwrite-add: m ≤ # kar ⊦ n < m → keyset(kar[n, ki], m) ++ kar[n] = keyset(kar, m) ++ ki;% ⊦ m ≤ m; (s)% ⊦ # kar[n, ki] = # kar; (s)% ⊦ m < n → m ≤ n; (s) Used terms: kar[n0], n1, kar[n1], n0, kar