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Proof step 6 from proof payload-copy-right-lower (previous step)

m + (nused0 + 1) + n < # zbrar, m < # copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), ∀ m, n, zbrar. m + nused0 + n < # zbrar → payload(copy(zbrar, m + nused0, zbrar, m + nused0 + 1, n), m, nused0) = payload(zbrar, m, nused0) ⊦ (copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n)[m].entry? ⊃ payload(copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), m + 1, nused0) [copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n)[m].key, copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n)[m].adr ] ;payload(copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), m + 1, nused0) ) = payload(zbrar, m, nused0 + 1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
m + (nused0 + 1) + n < # zbrar, m < # zbrar, ∀ m, n, zbrar. m + nused0 + n < # zbrar → payload(copy(zbrar, m + nused0, zbrar, m + nused0 + 1, n), m, nused0) = payload(zbrar, m, nused0) ⊦ (zbrar[m].entry? ⊃ payload(copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), m + 1, nused0)[zbrar[m].key, zbrar[m].adr] ;payload(copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), m + 1, nused0) ) = (zbrar[m].entry? ⊃ payload(zbrar, m + 1, nused0)[zbrar[m].key, zbrar[m].adr];payload(zbrar, m + 1, nused0))

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) );%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%n < n0 ⊦ (* n) ≠ m0 + (* n0); (s)% ⊦ m < m + n ↔ n ≠ 0; (s)%⊦ m0 < # zbrar → copy(zbrar0, n, zbrar, n0, m)[m0] = (m0 < n0 ∨ n0 + m ≤ m0 ⊃ zbrar[m0];zbrar0[m0 + n - n0]); (s)% ⊦ # copy(zbrar, m, zbrar0, m0, n) = # zbrar0; (s)