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Proof step 120 from proof payload-shift-left (previous step)

zbrar[n0 + 1] = mkzentry(key, adr), n0 + 1 < # zbrar, n0 < nused, n < # zbrar, nused < # zbrar, n0 < # zbrar, n < nused, n + 1 < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ n0 ⊦ zbrar[n].entry?, ∃ n1. ¬ nused < n1 ∧ zbrar[n1].entry? ∧ zbrar[n1].key = key

User applied rule exists right

And closed the goal!

Rule argument

pos: right 2 terms: n0 + 1 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ mkzentry(key, adr).entry?; (s)% ⊦ mkzentry(key, adr).key = key; (s) Used terms: n0 + 1