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Proof step 16 from proof gengft (previous step)

r -- mkfs(class, ty, fieldvar) ' ∈ st, okval(val, ty), r ∈ st, okval(st[r -- mkfs(class, ty, fieldvar) '], ty) ⊦ mkfs(class, ty, fieldvar) ' = _type, goodfieldandtype(r0, sk0, st[r -- mkfs(class, ty, fieldvar) ', val]) ↔ goodfieldandtype(r0, sk0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ is_fskey(sk) → (goodfieldandtype(r, sk, st) ↔ r -- sk ∈ st ∧ okval(st[r -- sk], sk .fs .type))
Proof step 4:
⊦ is_indexkey(sk) → ¬ goodfieldandtype(r, sk, st)
Proof step 15:
is_fskey(sk0), r -- mkfs(class, ty, fieldvar) ' ∈ st, okval(val, ty), r ∈ st, okval(st[r -- mkfs(class, ty, fieldvar) '], ty) ⊦ mkfs(class, ty, fieldvar) ' = _type, r0 -- sk0 ∈ st[r -- mkfs(class, ty, fieldvar) ', val] ∧ okval(st[r -- mkfs(class, ty, fieldvar) ', val][r0 -- sk0], sk0 .fs .type) ↔ goodfieldandtype(r0, sk0, st)

Rule argument

[crewrite-arg: good-field-field , F , [st, sk, r] → [st[r -- mkfs(class, ty, fieldvar) ', val], sk0, r0] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_fskey(sk) ↔ is_indexkey(sk)])], [EXTRATERMS : (st[r -- mkfs(class, ty, fieldvar) ', val], sk0, r0)]]