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Proof step 12 from proof update-in-03 (previous step)

∀ r, r0, st. r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0 ∧ fis0 ≠ [] ⊦ r ∈ update(r0, fv + fis0, st) ↔ r ∈ st ∨ r = r0 ∧ 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 11:
∀ r, r0, st. r ∈ update(r0, fis0, st) ↔ r ∈ st ∨ r = r0 ∧ fis0 ≠ [] ⊦ r ∈ (update(r0, fis0, st)[r0 -- fv .1, fv .2]) ↔ r ∈ st ∨ r = r0

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ fv ' ≠ []], [CSIMPSEQ : ⊦ ¬ fis + fis0 ≠ [] ↔ fis = [] ∧ fis0 = []], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]