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Proof step 9 from proof validFields-rec (conclusion)

⊦ validFields(r, (sk × val) ' + fis, st) ↔ validFields(r, fis, st) ∧ sk ≠ _length ∧ sk ≠ _type ∧ r -- sk ∈ st ∧ ¬ sk ∈ fis

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ validFields(r, fis, st) ↔ unique_al(fis) ∧ ¬ _type ∈ fis ∧ ¬ _length ∈ fis ∧ hasKeys(r, fis .keys, st)
Proof step 8:
⊦ unique_al((sk × val) ' + fis) ∧ ¬ _type ∈ (sk × val) ' + fis ∧ ¬ _length ∈ (sk × val) ' + fis ∧ hasKeys(r, ((sk × val) ' + fis) .keys, st) ↔ validFields(r, fis, st) ∧ sk ≠ _length ∧ sk ≠ _type ∧ r -- sk ∈ st ∧ ¬ sk ∈ fis

Rule argument

[crewrite-arg: validFields , F , [st, fis, r] → [st, (sk × val) ' + fis, r] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, (sk × val) ' + fis, r)]]