[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 16 from proof payload-shift-left (previous step)

zbrar[n] = mkzentry(key, adr), zbrar[n0] = mkzentry(key0, adr0), n0 < # zbrar, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n0 ≤ nused, n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = payload(zbrar, 0, nused + 1)[key0], key0 = key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
m + nused ≤ # zbrar, n < nused, zbrar[m + n] = mkzentry(key, adr), ∀ n0. n0 < n ∧ zbrar[m + n0].entry? → zbrar[m + n0].key ≠ key ⊦ payload(zbrar, m, nused)[key] = adr
Proof step 18:
zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), n < # zbrar, nused < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = payload(zbrar, 0, nused + 1)[key0], key0 = key, 0 + nused + 1 ≤ # zbrar ∧ n0 < nused + 1 ∧ zbrar[0 + n0] = mkzentry(key0, adr0) ∧ (∀ n1. n1 < n0 ∧ zbrar[0 + n1].entry? → zbrar[0 + n1].key ≠ key0)
Proof step 20:
zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), zbrar[0 + n0] = mkzentry(key0, adr0), n < # zbrar, nused < # zbrar, n0 < # zbrar, n0 < nused + 1, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused, 0 + nused + 1 ≤ # zbrar, ∀ n1. n1 < n0 ∧ zbrar[0 + n1].entry? → zbrar[0 + n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = key

Rule argument

spec: <toplevel> name: at-payload seq: m + nused ≤ # zbrar, n < nused, zbrar[m + n] = mkzentry(key, adr), ∀ n0. n0 < n ∧ zbrar[m + n0].entry? → zbrar[m + n0].key ≠ key ⊦ payload(zbrar, m, nused)[key] = adr subst: [n, adr, key, nused, m, zbrar] → [n0, adr0, key0, nused + 1, 0, zbrar] flags: <all paths>

Additional information

Used terms: n0, adr0, key0, nused + 1, 0, zbrar