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Proof step 9 from proof size-consp (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ p ∈ ps ↔ (∃ ps0. ps = ps0 ++ p ∧ ¬ p ∈ ps0)
Proof step 11:
∃ ps0. ps = ps0 ++ p ∧ ¬ p ∈ ps0, ∀ ps0, str. # ps0 < # ps → true → #(str + ps0) = # ps0 ⊦ #(str + ps) = # ps, # ps = 0

Rule argument

spec: set-basic, inst: pathset name: indef seq: ⊦ p ∈ ps ↔ (∃ ps0. ps = ps0 ++ p ∧ ¬ p ∈ ps0) subst: [ps, p] → [ps, p] flags: <all paths>

Additional information

Used terms: ps, p