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Proof step 11 from proof good-field-subset (previous step)

st ⊆ st0, r -- sk ∈ st, r ∈ st ⊦ goodfieldandtype(r, sk, st0) ↔ goodfieldandtype(r, sk, st)

User applied rule insert rewrite lemma

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 10:
is_fskey(sk), st ⊆ st0, r -- sk ∈ st, r ∈ st ⊦ goodfieldandtype(r, sk, st0) ↔ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type)

Rule argument

[crewrite-arg: good-field-field, F, [st, sk, r] → [st, sk, r]]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])], [EXTRATERMS : (st, sk, r)]]