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Proof step 4 from proof payload-copy-right-lower (previous step)

m + (nused0 + 1) + n < # zbrar, ∀ m, n, zbrar. m + nused0 + n < # zbrar → payload(copy(zbrar, m + nused0, zbrar, m + nused0 + 1, n), m, nused0) = payload(zbrar, m, nused0) ⊦ payload(copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n), m, nused0 + 1) = payload(zbrar, m, nused0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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))
Proof step 6:
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)

Rule argument

spec: <toplevel> name: payload-rec seq: ⊦ 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) ) subst: [nused, m, zbrar] → [nused0, m, copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n)] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # copy(zbrar, m, zbrar0, m0, n) = # zbrar0; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: nused0, m, copy(zbrar, m + nused0 + 1, zbrar, 2 + m + nused0, n)