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Proof step 29 from proof no-dups-keyset-size (previous step)

# keyset(kar, m0) = m0, kar[m1] = kar[m], m < # kar, m1 < # kar, m0 < # kar, m ≤ m0, m1 ≤ m0, ∀ m2, m1. m2 < # kar ∧ m2 < m0 ∧ m1 < # kar ∧ m1 < m0 ∧ m2 ≠ m1 → kar[m2] ≠ kar[m1] ⊦ m1 = m, ∃ m. m < m0 ∧ kar[m0] = kar[m]

User applied rule all left

And obtained the following new goals

Proof step 30:
# 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]

Rule argument

pos: left 8 terms: m1, m abort: F discard: T computed: T

Additional information

Used terms: m1, m