Research proof index

The following two signs are equal for i.succAbove k < i. The sign signInsertSome φ φs φsΛ i k which is constructed as follows: 1a. For each contracted pair {a1, a2} in φsΛ with a1 < a2 the sign 𝓢(φ, φₐ₂) if a₁ < i ≤ a₂ and a₁ < k. 1b. For each contracted pair {a1, a2} in φsΛ with a1 < a2 the sign 𝓢(φⱼ, φₐ₂) if a₁ < k < a₂ and `...

The following two signs are equal for i < i.succAbove k. The sign signInsertSome φ φs φsΛ i k which is constructed as follows: 1a. For each contracted pair {a1, a2} in φsΛ with a1 < a2 the sign 𝓢(φ, φₐ₂) if a₁ < i ≤ a₂ and a₁ < k. 1b. For each contracted pair {a1, a2} in φsΛ with a1 < a2 the sign 𝓢(φⱼ, φₐ₂) if a₁ < k < a₂ and `...