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Proof step 18 from proof range-put (previous step)

nused ≤ # zbrar ⊦ # zbrar = 0, nused = 0, zbrar[0].key < key, (key0 ∈ key-range(zbrar, 0, nused, ri[key, adr]) ↔ key0 = key ∨ key0 ∈ key-range(zbrar, 0, nused, ri)) ∧ (key0 ∈ key-range(zbrar, 0, nused, ri[key, adr]) → ri[key, adr][key0] = key-range(zbrar, 0, nused, ri)[key, adr][key0])

User applied rule constructor cut

And obtained the following new goals

Proof step 19:
nused = nused0 +1, nused ≤ # zbrar ⊦ # zbrar = 0, nused = 0, zbrar[0].key < key, (key0 ∈ key-range(zbrar, 0, nused, ri[key, adr]) ↔ key0 = key ∨ key0 ∈ key-range(zbrar, 0, nused, ri)) ∧ (key0 ∈ key-range(zbrar, 0, nused, ri[key, adr]) → ri[key, adr][key0] = key-range(zbrar, 0, nused, ri)[key, adr][key0])

Rule argument

var: nused

Additional information

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