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Proof step 3 from proof payload-shift-left (previous step)

n < # zbrar, nused < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = (zbrar[n].entry? ⊃ payload(zbrar, 0, nused + 1) -- zbrar[n].key;payload(zbrar, 0, nused + 1))

User applied rule case distinction

And obtained the following new goals

Proof step 4:
zbrar[n].entry?, nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = payload(zbrar, 0, nused + 1) -- zbrar[n].key
Proof step 72:
nused < # zbrar, n < # zbrar, sorted(zbrar, 0, nused + 1), n ≤ nused ⊦ payload(shl(zbrar, n, nused + 1), 0, nused) = payload(zbrar, 0, nused + 1), zbrar[n].entry?

Rule argument

pos: right 1

Proof step 3 from proof payload-shift-left (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information