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Proof step 8 from proof sorted-eq-entry (previous step)

zbrar[m1] = mkzentry(key, adr1), zbrar[m0] = mkzentry(key, adr0), m0 < # zbrar, m1 < # zbrar, m0 < m, m1 < m, m ≤ # zbrar, m1 ≤ m0, ∀ m2, m3. m2 < m3 ∧ m3 < m → zbrar[m2].key < zbrar[m3].key ⊦ m0 = m1 ∧ adr0 = adr1

User applied rule all left

And closed the goal!

Rule argument

pos: left 9 terms: m1, m0 abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ mkzentry(key, adr).key = key; (s)% ⊦ ¬ key < key; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ mkzentry(key, adr) = mkzentry(key0, adr0) ↔ key = key0 ∧ adr = adr0; (ws) Used terms: m1, m0