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Proof step 3 from proof blast-first (previous step)

x = a0 + y, a ∈ x.butlast, a ∈ x ⊦ x.butlast.first = a0, x = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
a ∈ (a0 ' + y).butlast, a = a0 ∨ a ∈ y ⊦ (a0 ' + y).butlast.first = a0

Rule argument

Additional information

Used simplifier rules: bin-01: x ≠ [] ⊦ a ∈ x.butlast → a ∈ x;%in-rec: ⊦ a ∈ b ' + x ↔ ¬ ¬(a = b ∨ a ∈ x); from specification list%a: ⊦ (x + y) + z = x + y + z; from specification list%e-01: ⊦ a ' + x ≠ []; from specification list%c: ⊦ a + x = a ' + x; from specification list