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Proof step 16 from proof keys-put-in (previous step)

sk ∈ fv ' + fis0, ∀ sk, val. sk ∈ fis0 → fis0[sk, val] .keys = fis0 .keys ⊦ (fv ' + fis0)[sk, val] .keys = fv .1 ' + fis0 .keys

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 15:
fv = sk0 × val0, sk ∈ fv ' + fis0, ∀ sk, val. sk ∈ fis0 → fis0[sk, val] .keys = fis0 .keys ⊦ (fv ' + fis0)[sk, val] .keys = sk0 ' + fis0 .keys

Rule argument

[speclemmaarg: ,sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val ,[fv, sk, val] → [fv, sk0, val0] ,T ,pair ,fieldinit ,elim ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ sk = fv .1 ∧ val = fv .2 ↔ fv = sk × val])], [EXTRATERMS : (fv, sk0, val0)]]