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Proof step 9 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, fv + fis0, st) ↔ r0 -- sk ∈ st, sk ∈ fv + fis0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
⊦ update(r, fv ' + fis, st) = (update(r, fis, st)[r -- fv .1, fv .2])
Proof step 8:
∀ r0, sk, r, st. (r0 -- sk ∈ update(r, fis0, st) ↔ r0 -- sk ∈ st) ∨ sk ∈ fis0 ⊦ r0 -- sk ∈ (update(r, fis0, st)[r -- fv .1, fv .2]) ↔ r0 -- sk ∈ st, sk ∈ fv ', sk ∈ fis0

Rule argument

[emptyarg]

Additional information

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