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Proof step 3 from proof ri-inj-write (previous step)

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

Heuristic weak cut applied rule cut formula

And obtained the following new goals

Proof step 4:
ri[key, adr][key0] = ri[key, adr][key1], key1 ∈ ri[key, adr], key0 ∈ ri[key, adr], ∀ key0, key1. key0 ∈ ri ∧ key1 ∈ ri ∧ ri[key0] = ri[key1] → key0 = key1 ⊦ key0 = key1, key1 = key, adr ∈ ri

Rule argument

fma: key1 = key

Additional information

Used simplifier rules: ⊦ key ≠ key0 → ri[key0, adr][key] = ri[key]; (s)% ⊦ ri[key, adr][key] = adr; (s)% ⊦ key ≠ key0 → (key ∈ ri[key0, adr] ↔ key ∈ ri); (s)% ⊦ key ∈ ri[key, adr]; (s)%key ∈ ri ⊦ ri[key] ∈ ri; (s) Used formulas: key1 = key