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Proof step 7 from proof validFields-put-01 (previous step)

⊦ unique_al(fis) ∧ ¬ _type ∈ fis ∧ ¬ _length ∈ fis ∧ hasKeys(r, fis .keys, st[r -- sk, val]) ↔ unique_al(fis) ∧ ¬ _type ∈ fis ∧ ¬ _length ∈ fis ∧ hasKeys(r, fis .keys, st), sk ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ¬ sk ∈ sks → (hasKeys(r, sks, st[r -- sk, val]) ↔ hasKeys(r, sks, st))
Proof step 6:
¬ ¬ sk ∈ fis .keys ⊦ unique_al(fis) ∧ ¬ _type ∈ fis ∧ ¬ _length ∈ fis ∧ hasKeys(r, fis .keys, st[r -- sk, val]) ↔ unique_al(fis) ∧ ¬ _type ∈ fis ∧ ¬ _length ∈ fis ∧ hasKeys(r, fis .keys, st), sk ∈ fis

Rule argument

[crewrite-arg: hasKeys-put-02 , F , [val, sk, st, sks, r] → [val, sk, st, fis .keys, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (val, sk, st, fis .keys, r)]]