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Proof step 1 from proof len-04 (conclusion)

⊦ a ' + x0 = x + b ' + y + c ' + z → # x + # z < # x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
a ' + x0 = x + b ' + y + c ' + z, # x0 ≤ # x + # z, a ∈ x ∨ a = b ∨ a ∈ y ∨ a = c ∨ a ∈ z ⊦

Rule argument

Additional information

Used simplifier rules: in-14: ⊦ a ' + x = y → a ∈ y;%a: ⊦ (x + y) + z = x + y + z;%in-append: ⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y);%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x);%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat