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Proof step 100 from proof payload-shift-left (previous step)

zbrar[n2 + 1] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n2 < nused, n2 + 1 < # zbrar, n2 < # zbrar, sorted(zbrar, 0, nused + 1), key ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ n2 + 1, n ≤ nused, ∀ n0. ¬ n2 < n0 ∧ zbrar[n0].entry? → zbrar[n0].key ≠ key ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key] = adr, zbrar[n].entry?, (n2 < n ⊃ zbrar[n2];mkzentry(key, adr)) = mkzentry(key, adr) ∧ (n0 < n2 ∧ (n0 < n ∨ nused ≤ n0 ⊃ zbrar[n0];zbrar[n0 + 1]).entry? → (n0 < n ∨ nused ≤ n0 ⊃ zbrar[n0];zbrar[n0 + 1]).key ≠ key)

Heuristic nonsplitting cut applied rule cut formula

And obtained the following new goals

Rule argument

fma: n2 < n

Additional information

Used simplifier rules: ⊦ m < n → (n ≤ m + 1 ↔ n = m + 1); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%eqle-one: ⊦ m = n + 1 ∧ n < n0 → m ≤ n0; (forward) from specification nat%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m + 1 ≠ 0; (s)% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ ¬ n < n; (s)% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ n < n0 → (n0 < n ↔ false); (ss)% ⊦ mkzentry(key, adr).entry?; (s) Used formulas: n2 < n