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Proof step 7 from proof l (previous step)

a ∈ x0, ∀ m, a. # x0 = m + 1 ∧ a ∈ x0 → #(x0 -1l a) = m ∨ x0 = [] ⊦ 1 + #(x0 -1l a) = # x0, a = a0

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 8:
a ∈ x0, ∀ m, a. # x0 = m + 1 ∧ a ∈ x0 → #(x0 -1l a) = m ∨ x0 = [] ⊦ 1 + #(x0 -1l a) = # x0, a = a0, x0 = []

Rule argument

fma: x0 = []

Additional information

Used simplifier rules: del1-e: ⊦ [] -1l a = [];% ⊦ # [] = 0; (s)% ⊦ ¬ a ∈ []; (s) Used formulas: x0 = []