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Proof step 10 from proof validfieldlist-put-statfield (previous step)

∀ r, sk, str, st, val. r ≠ jvmref ∨ ¬ sk ∈ sks0 → (validfieldlist(str, r, sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sks0, st)), r ≠ jvmref ∨ ¬ sk ∈ sk0 + sks0 ⊦ validfieldlist(str, r, sk0 + sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sk0 + sks0, st)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
∀ r, sk, str, st, val. r ≠ jvmref ∨ ¬ sk ∈ sks0 → (validfieldlist(str, r, sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sks0, st)), r ≠ jvmref ∨ sk ≠ sk0 ∧ ¬ sk ∈ sks0 ⊦ validfieldlist(str, r, sk0 ' + sks0, st[jvmref -- sk, val]) ↔ validfieldlist(str, r, sk0 ' + sks0, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ ¬ sk ∈ sk0 ' + sks ↔ sk ≠ sk0 ∧ ¬ sk ∈ sks], [CSIMPSEQ : ⊦ sk + sks = sk ' + sks])]]