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Proof step 9 from proof validFields-putfis (previous step)

unique_al(fis), r -- sk ∈ st, r ∈ st, ∀ sk0. sk0 ∈ fis .keys → r -- sk0 ∈ st ⊦ _length = sk, _type = sk, _length ∈ fis, _type ∈ fis, hasKeys(r, fis .keys, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ hasKeys(r, sks, st) ↔ (∀ sk. sk ∈ sks → r -- sk ∈ st)
Proof step 8:
unique_al(fis), r -- sk ∈ st, r ∈ st, ∀ sk0. sk0 ∈ fis .keys → r -- sk0 ∈ st ⊦ _length = sk, _type = sk, _length ∈ fis, _type ∈ fis, ∀ sk. sk ∈ fis .keys → r -- sk ∈ st

Rule argument

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

Additional information

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