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Proof step 12 from proof payload-drop-lower (previous step)

zbrar[m + n] = mkzentry(key, adr), m + n < # zbrar, m + n + nused0 < # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ payload(zbrar[m, zbr], (m + n) + 1, nused0)[key, adr] = payload(zbrar, (m + n) + 1, nused0)[key, adr], n = 0

User applied rule all left

And closed the goal!

Rule argument

pos: left 4 terms: m, 1 + n, zbrar, zbr abort: F discard: F computed: F

Additional information

Used simplifier rules: ⊦ m + 1 ≤ n ↔ m < n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + 1 ≠ 0; (s) Used terms: m, 1 + n, zbrar, zbr