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Proof step 3 from proof keys-put-notin (conclusion)

⊦ ¬ sk ∈ fis → fis[sk, val] .keys = fis .keys + sk

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ (fis + fis0) .keys = fis .keys + fis0 .keys
Proof step 2:
⊦ fv ' .keys = fv .1 '

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sks + sks0 = sks + sks1 ↔ sks0 = sks1], [CSIMPSEQ : ⊦ sks + sk = sks + sk '], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ (sk × val) .1 = sk], [CSIMPSEQ : ⊦ ¬ sk ∈ fis → fis[sk, val] = fis + (sk × val) '])]]