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Proof step 5 from proof good-field-def (conclusion)

⊦ goodfieldandtype(r, sk, st) ↔ is_fskey(sk) ∧ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1:
⊦ is_fskey(sk) → (goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type))
Proof step 2:
⊦ is_indexkey(sk) → ¬ goodfieldandtype(r, sk, st)
Proof step 3:
⊦ ¬ r -- sk ∈ st → ¬ goodfieldandtype(r, sk, st)
Proof step 4:
⊦ r -- sk ∈ st → (goodfieldandtype(r, sk, st) ↔ ¬ ¬ (is_fskey(sk) ∧ okval(st[r -- sk], sk .fs .type)))

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])]]