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Proof step 9 from proof payload-copy-right-upper (previous step)

n0 + 1 < # zbrar, n0 + nused0 + 1 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ (zbrar[n0].entry? ⊃ payload(copy(zbrar, n0, zbrar, n0 + 1, nused0 + 1), 2 + n0, nused0)[zbrar[n0].key, zbrar[n0].adr] ;payload(copy(zbrar, n0, zbrar, n0 + 1, nused0 + 1), 2 + n0, nused0) ) = payload(zbrar, n0, nused0 + 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ copy(zbrar, m, zbrar0, m0, n + 1) = copy(zbrar, m + 1, zbrar0, m0 + 1, n)[m0, zbrar[m]]
Proof step 11:
n0 + nused0 + 1 < # zbrar, n0 + 1 < # zbrar, ∀ n, zbrar. n + nused0 < # zbrar → payload(copy(zbrar, n, zbrar, n + 1, nused0), n + 1, nused0) = payload(zbrar, n, nused0) ⊦ (zbrar[n0].entry? ⊃ payload(copy(zbrar, n0 + 1, zbrar, (n0 + 1) + 1, nused0)[n0 + 1, zbrar[n0]], 2 + n0, nused0)[zbrar[n0].key, zbrar[n0].adr] ;payload(copy(zbrar, n0 + 1, zbrar, (n0 + 1) + 1, nused0)[n0 + 1, zbrar[n0]], 2 + n0, nused0) ) = payload(zbrar, n0, nused0 + 1)

Rule argument

spec: array-copy, inst: zbranch-array name: copy-rec seq: ⊦ copy(zbrar, m, zbrar0, m0, n + 1) = copy(zbrar, m + 1, zbrar0, m0 + 1, n)[m0, zbrar[m]] subst: [n, m0, zbrar0, m, zbrar] → [nused0, n0 + 1, zbrar, n0, zbrar] flags: <all paths>

Additional information

Used terms: nused0, n0 + 1, zbrar, n0, zbrar