[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 21 from proof payload-shift-left (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 22:
zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, n0 < n, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = key
Proof step 27:
zbrar[n0] = mkzentry(key0, adr0), zbrar[n] = mkzentry(key, adr), nused < # zbrar, n < # zbrar, n0 < # zbrar, sorted(zbrar, 0, nused + 1), key0 ∈ payload(shl(zbrar, n, nused + 1), 0, nused), n ≤ nused, n0 ≤ nused, ∀ n1. n1 < n0 ∧ zbrar[n1].entry? → zbrar[n1].key ≠ key0 ⊦ payload(shl(zbrar, n, nused + 1), 0, nused)[key0] = adr0, key0 = key, n0 < n

Rule argument

fma: n0 < n

Additional information

Used formulas: n0 < n