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Proof step 7 from proof update-keyin (previous step)

∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- (sk0 × val) .1, (sk0 × val) .2]) ↔ r0 -- sk ∈ st, sk ∈ (sk0 × val) ', sk ∈ fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- sk0, val]) ↔ r0 -- sk ∈ st, sk = sk0, sk ∈ fis0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ sk ∈ (sk0 × val) ' ↔ sk = sk0], [CSIMPSEQ : ⊦ (sk × val) .2 = val], [CSIMPSEQ : ⊦ (sk × val) .1 = sk])]]