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Proof step 8 from proof size-consp (previous step)

∀ ps0, str. # ps0 < # ps → true → #(str + ps0) = # ps0 ⊦ #(str + ps) = # ps, # ps = 0, ∀ p. p ∈ ps ↔ p ∈ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
p ∈ ps, ∀ ps0, str. # ps0 < # ps → true → #(str + ps0) = # ps0 ⊦ # ps = 0, #(str + ps) = # ps

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ p ∈ ∅; (s)