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Proof step 13 from proof size-consp (previous step)

∀ ps1, str. # ps1 < #(ps0 ++ p) → true → #(str + ps1) = # ps1 ⊦ #((str + ps0) ++ (str ' + p)) = # ps0 + 1, p ∈ ps0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ p ∈ ps → #(ps ++ p) = # ps + 1
Proof step 15:
⊦ p ∈ str + ps ↔ p ≠ ε ∧ p.head = str ∧ p.tail ∈ ps
Proof step 16:
∀ ps1, str. # ps1 < #(ps0 ++ p) → true → #(str + ps1) = # ps1 ⊦ #(str + ps0) + 1 = # ps0 + 1, p ∈ ps0, str ' + p ∈ str + ps0

Rule argument

spec: set-basic, inst: pathset name: Size-insert seq: ⊦ ¬ p ∈ ps → #(ps ++ p) = # ps + 1 subst: [p, ps] → [str ' + p, str + ps0] flags: <all paths>

Additional information

Used simplifier rules: in-consp: ⊦ p ∈ str + ps ↔ p ≠ ε ∧ p.head = str ∧ p.tail ∈ ps;% ⊦ p ∈ ps → ps ++ p = ps; (s)% ⊦ str ' + p ≠ ε; (s)%a: ⊦ (p + p0) + p1 = p + p0 + p1; from specification list[path]% ⊦ (str ' + p).head = str; (s)% ⊦ (str ' + p).tail = p; (s) Used terms: str ' + p, str + ps0