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Proof step 30 from proof no-dups-keyset-size (previous step)

# keyset(kar, m0) = m0, kar[m1] = kar[m], m0 < # kar, m1 < # kar, m < # kar, m1 ≤ m0, m ≤ m0, m1 < # kar ∧ m1 < m0 ∧ m < # kar ∧ m < m0 ∧ m1 ≠ m → kar[m1] ≠ kar[m] ⊦ m1 = m, ∃ m. m < m0 ∧ kar[m0] = kar[m]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 31:
# keyset(kar, m0) = m0, kar[m1] = kar[m], m < # kar, m1 < # kar, m0 < # kar, m ≤ m0, m1 ≤ m0 ⊦ m1 = m, ∃ m. m < m0 ∧ kar[m0] = kar[m], m1 < m0 ∧ m < m0

Proof step 30 from proof no-dups-keyset-size (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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