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Proof step 7 from proof always-noincrease-stable (previous step)

□ (A ≪ a ∨ A = a), □ ⟨a1 := A⟩ (□ (A ≪ a1 ∨ A = a1)), □ (A'' ≪ A ∨ A'' = A), a = A, a0 = A, A'' ≪ A ∨ A'' = A ⊦ ◇ A ≪ a0, ◇ □ A'' = A, □ A'' = A

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
□ ⟨a1 := A⟩ (□ (A ≪ a1 ∨ A = a1)), □ (A'' ≪ A ∨ A'' = A), □ A = a, a = A, A'' ≪ A ∨ A'' = A ⊦ ◇ □ A'' = A, □ A'' = A

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ a ≪ a; (s)