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Proof step 9 from proof update-keyin-01 (previous step)

∀ r, sk, r0, st. r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis0 ⊦ r -- sk = r0 -- sk0 ∨ r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ (sk = sk0 ∨ sk ∈ fis0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
∀ r, sk, r0, st. r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ sk ∈ fis0 ⊦ r = r0 ∧ sk = sk0 ∨ r -- sk ∈ update(r0, fis0, st) ↔ r -- sk ∈ st ∨ r = r0 ∧ (sk = sk0 ∨ sk ∈ fis0)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0])]]