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Proof step 8 from proof payload-drop-lower (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 9:
zbrar[m + n].entry?, 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)[zbrar[m + n].key, zbrar[m + n].adr] = (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
Proof step 13:
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) ⊦ n = 0, 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)), zbrar[m + n].entry?

Rule argument

pos: right 1

Proof step 8 from proof payload-drop-lower (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information