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Proof step 17 from proof keys-put-in (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ (fis + fis0) .keys = fis .keys + fis0 .keys
Proof step 4:
⊦ fv ' .keys = fv .1 '
Proof step 16:
sk ∈ fv ' + fis0, ∀ sk, val. sk ∈ fis0 → fis0[sk, val] .keys = fis0 .keys ⊦ (fv ' + fis0)[sk, val] .keys = fv .1 ' + fis0 .keys

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]