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Proof step 5 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, 0 + m ≤ # zbrar, ∀ m0, m1. m0 < m1 ∧ m1 < m → zbrar[0 + m0].key < zbrar[0 + m1].key ⊦ m0 = m1 ∧ adr0 = adr1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
zbrar[m0] = mkzentry(key, adr0), zbrar[m1] = mkzentry(key, adr1), m1 < m, m0 < m, m1 < # zbrar, m0 < # zbrar, m ≤ # zbrar, ∀ m2, m3. m2 < m3 ∧ m3 < m → zbrar[m2].key < zbrar[m3].key ⊦ m0 = m1 ∧ adr0 = adr1

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)