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Proof step 8 from proof update-in-03 (previous step)

∀ r, r0, st. r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0 ∧ fis0 ≠ [] ⊦ r = r0 ∨ r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0

User applied rule case distinction

And obtained the following new goals

Proof step 5:
r = r0 ∨ r ∈ update(r0, fis0, st), ∀ r, r0, st. r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0 ∧ fis0 ≠ [] ⊦ r ∈ st ∨ r = r0
Proof step 7:
r ∈ st ∨ r = r0, ∀ r, r0, st. r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0 ∧ fis0 ≠ [] ⊦ r = r0 ∨ r ∈ update(r0, fis0, st)

Rule argument

[CASEDARG : pos: right 1, ()]

Additional information

[[CONCRETESIMPRULES : ()]]