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Proof step 26 from proof keys-shift-left (previous step)

zbrar[n0 + 1].key = zbrar[n].key, n0 < # zbrar, n < # zbrar, n0 < nused, n0 + 1 < # zbrar, n < nused, n + 1 < # zbrar, nused < # zbrar, n ≤ n0, ∀ m, m0. m < m0 ∧ ¬ nused < m0 → zbrar[m].key < zbrar[m0].key ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 10 terms: n, n0 + 1 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%lel: ⊦ key < key0 ∧ key = key1 → key1 < key0; (forward) from specification oelem[key-order]% ⊦ ¬ key < key; (s) Used terms: n, n0 + 1