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Proof step 11 from proof okfieldinits-index (previous step)

∀ sk, class. ¬ (sk ∈ fis0 .keys ∧ okfieldinits(class, fis0) ∧ is_indexkey(sk)), sk ∈ (fv + fis0) .keys, okfieldinits(class, fv + fis0), is_indexkey(sk) ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 10:
is_indexkey(sk), okfieldinits(class, fv ' + fis0), ∀ sk0, class0. ¬ sk0 ∈ fis0 .keys ∨ ¬ okfieldinits(class0, fis0) ∨ is_fskey(sk0) ⊦ sk ≠ fv .1 ∧ ¬ sk ∈ fis0 .keys

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_indexkey(sk) ↔ is_fskey(sk)], [CSIMPSEQ : ⊦ (sks + sks0) + sks1 = sks + sks0 + sks1], [CSIMPSEQ : ⊦ sk ∈ sk0 ' ↔ sk = sk0], [CSIMPSEQ : ⊦ sk ∈ sks + sks0 ↔ ¬ ¬ (sk ∈ sks ∨ sk ∈ sks0)], [CSIMPSEQ : ⊦ (fis + fis0) + fis1 = fis + fis0 + fis1], [CSIMPSEQ : ⊦ fv ' .keys = fv .1 '], [CSIMPSEQ : ⊦ (fis + fis0) .keys = fis .keys + fis0 .keys], [CSIMPSEQ : ⊦ fv + fis = fv ' + fis])]]