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Proof step 4 from proof del-this (previous step)

⊦ (key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key) ∧ (key0 ∈ ri[key, adr] ⊖ key → (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0])

User applied rule cut formula

And obtained the following new goals

Proof step 5:
key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key ⊦ (key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key) ∧ (key0 ∈ ri[key, adr] ⊖ key → (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0])
Proof step 13:
⊦ key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key, (key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key) ∧ (key0 ∈ ri[key, adr] ⊖ key → (ri[key, adr] ⊖ key)[key0] = (ri ⊖ key)[key0])

Rule argument

fma: key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key

Additional information

Used formulas: key0 ∈ ri[key, adr] ⊖ key ↔ key0 ∈ ri ⊖ key