| ⊦ key ∈ ks, (key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key) ∧ (key0 ∈ (ri ⊖ key) ⊖ ks → ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0]) |
key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key ⊦ key ∈ ks, (key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key) ∧ (key0 ∈ (ri ⊖ key) ⊖ ks → ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0])
⊦ key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key, key ∈ ks, (key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key) ∧ (key0 ∈ (ri ⊖ key) ⊖ ks → ((ri ⊖ key) ⊖ ks)[key0] = ((ri ⊖ ks) ⊖ key)[key0])
Used formulas: key0 ∈ (ri ⊖ key) ⊖ ks ↔ key0 ∈ (ri ⊖ ks) ⊖ key