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Proof step 7 from proof payload-drop-lower (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
m + n + nused0 < # zbrar, m + n < # zbrar, ∀ m, n, zbrar, zbr. m + n + nused0 ≤ # zbrar → n = 0 ∨ payload(zbrar[m, zbr], m + n, nused0) = payload(zbrar, m + n, nused0) ⊦ (zbrar[m + n].entry? ⊃ payload(zbrar[m, zbr], (m + n) + 1, nused0)[zbrar[m + n].key, zbrar[m + n].adr] ;payload(zbrar[m, zbr], (m + n) + 1, nused0) ) = (zbrar[m + n].entry? ⊃ payload(zbrar, (m + n) + 1, nused0)[zbrar[m + n].key, zbrar[m + n].adr];payload(zbrar, (m + n) + 1, nused0)), n = 0

Rule argument

Additional information

Used simplifier rules: payload-rec: ⊦ m < # zbrar → payload(zbrar, m, nused + 1) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused)[zbrar[m].key, zbrar[m].adr] ;payload(zbrar, m + 1, nused) );% ⊦ # zbrar[n, zbr] = # zbrar; (s)%m ≠ n ⊦ zbrar[m, zbr][n] = zbrar[n]; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m = m + n ↔ n = 0; (s)