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Proof step 6 from proof replay-orphans-del (previous step)

⊦ key ∈ ro, (key0 ≠ key ∧ key0 ∈ ri ⊖ ro ↔ key0 ∈ (ri -- key) ⊖ ro) ∧ (key0 ≠ key ∧ key0 ∈ ri ⊖ ro → (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0])

User applied rule cut formula

And obtained the following new goals

Proof step 7:
key0 ∈ (ri ⊖ ro) -- key ↔ key0 ∈ (ri -- key) ⊖ ro ⊦ key ∈ ro, (key0 ≠ key ∧ key0 ∈ ri ⊖ ro ↔ key0 ∈ (ri -- key) ⊖ ro) ∧ (key0 ≠ key ∧ key0 ∈ ri ⊖ ro → (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0])
Proof step 18:
⊦ key0 ∈ (ri ⊖ ro) -- key ↔ key0 ∈ (ri -- key) ⊖ ro, key ∈ ro, (key0 ≠ key ∧ key0 ∈ ri ⊖ ro ↔ key0 ∈ (ri -- key) ⊖ ro) ∧ (key0 ≠ key ∧ key0 ∈ ri ⊖ ro → (ri ⊖ ro)[key0] = ((ri -- key) ⊖ ro)[key0])

Rule argument

fma: key0 ∈ (ri ⊖ ro) -- key ↔ key0 ∈ (ri -- key) ⊖ ro

Additional information

Used formulas: key0 ∈ (ri ⊖ ro) -- key ↔ key0 ∈ (ri -- key) ⊖ ro