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Proof step 8 from proof at-range (previous step)

key ∈ key-range(zbrar, 0, nused, ri), nused ≤ # zbrar ⊦ # zbrar = 0, key-range(zbrar, 0, nused, ri)[key] = ri[key], nused = 0

User applied rule constructor cut

And obtained the following new goals

Proof step 9:
nused = nused0 +1, key ∈ key-range(zbrar, 0, nused, ri), nused ≤ # zbrar ⊦ # zbrar = 0, key-range(zbrar, 0, nused, ri)[key] = ri[key], nused = 0

Rule argument

var: nused

Additional information

Used simplifier rules: nat freely generated by 0, +1;;