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Proof step 3 from proof keyset-subarray-eq (previous step)

subarray(kar0, 0, m) = subarray(kar1, 0, m), m ≤ # kar0, m ≤ # kar1 ⊦ keyset(kar0, m) = keyset(kar1, m)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
subarray(kar0, 0, m0 +1) = subarray(kar1, 0, m0 +1), m0 +1 ≤ # kar1, m0 +1 ≤ # kar0, ∀ kar0, kar1. subarray(kar0, 0, m0) = subarray(kar1, 0, m0) ∧ m0 ≤ # kar0 ∧ m0 ≤ # kar1 → keyset(kar0, m0) = keyset(kar1, m0) ⊦ keyset(kar0, m0 +1) = keyset(kar1, m0 +1)

Rule argument

indvar: m

Additional information

Used simplifier rules: keyset-base: ⊦ keyset(kar, 0) = ∅;%nat freely generated by 0, +1;;%# kar = n ⊦ subarray(kar, 0, n) = kar; (s)