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Proof step 5 from proof ri-inj-write (previous step)

ri[key, adr][key0] = ri[key1], key0 ∈ ri[key, adr], key1 ∈ ri, ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key1, key1 = key, adr ∈ ri

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 6:
ri[key, adr][key0] = ri[key1], key1 ∈ ri, key0 ∈ ri[key, adr], ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key1, key0 = key, key1 = key, adr ∈ ri

Rule argument

fma: key0 = key

Additional information

Used simplifier rules: ⊦ ri[key, adr][key] = adr; (s)% ⊦ key ∈ ri[key, adr]; (s)%key ∈ ri ⊦ ri[key] ∈ ri; (s) Used formulas: key0 = key