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Proof step 16 from proof in-payload (previous step)

zbrar[m] = mkzentry(key0, adr), m < # zbrar, m + nused0 < # zbrar, key = key0 ∨ n < nused0 ∧ zbrar[(m + 1) + n].entry? ∧ zbrar[(m + 1) + n].key = key ⊦ ∃ n. ¬ nused0 < n ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key

User applied rule case distinction

And obtained the following new goals

Proof step 17:
zbrar[m] = mkzentry(key0, adr), key = key0, m + nused0 < # zbrar, m < # zbrar ⊦ ∃ n. ¬ nused0 < n ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key
Proof step 19:
zbrar[(m + 1) + n].key = key, zbrar[m] = mkzentry(key0, adr), zbrar[(m + 1) + n].entry?, m + nused0 < # zbrar, m < # zbrar, n < nused0 ⊦ ∃ n. ¬ nused0 < n ∧ zbrar[m + n].entry? ∧ zbrar[m + n].key = key

Rule argument

pos: left 4

Proof step 16 from proof in-payload (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information