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Proof step 29 from proof validFields-putfis (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ hasKeys(r, sks, st) ↔ (∀ sk. sk ∈ sks → r -- sk ∈ st)
Proof step 28:
hasKeys(r, fis .keys, st), r -- sk ∈ st, unique_al(fis), r ∈ st ⊦ sk = _type, sk = _length, _length ∈ fis, _type ∈ fis, ∀ sk0. sk0 ∈ fis[sk, val] .keys → r -- sk0 ∈ st

Rule argument

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

Additional information

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