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Proof step 3 from proof gft-union (conclusion)

⊦ ¬ r ∈ st .refs → (goodfieldandtype(r, sk, st ∪ st0) ↔ goodfieldandtype(r, sk, st0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)
Proof step 2:
⊦ goodfieldandtype(r, sk, st) ↔ ¬ ¬ (is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ is_indexkey(sk) → ¬ is_fskey(sk)], [CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)], [CSIMPSEQ : ⊦ ¬ r ∈ st .refs → (st ∪ st0)[r -- sk] = st0[r -- sk]], [CSIMPSEQ : ⊦ ¬ r ∈ st .refs → ( r -- sk ∈ st ∪ st0 ↔ r -- sk ∈ st0)])]]