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Proof step 49 from proof validref-putrkvs (previous step)

sk .fs = mkfs(class, ty0, fieldvar), validval(str, val, st[r0 -- _type] .type .type, st), validref(str, r, ty, st), validvals(str, rkvs0, st), is_indexkey(sk), ∀ str, r, ty, st. validref(str, r, ty, st) ∧ validvals(str, rkvs0, st) → validref(str, r, ty, st[rkvs0]) ⊦ validref(str, r, ty, st[r0 -- sk, val]), validref(str, r, ty, st[r0 -- sk, val][rkvs0]), is_referencevalue(val), okval(val, st[r0 -- _type] .type .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 48:
⊦ validval(str, val, ty, st) ↔ okval(val, ty) ∧ (is_referencevalue(val) → validrefval(str, val, ty, st))

Rule argument

[crewrite-arg: validval-def , F , [st, ty, val, str] → [st, st[r0 -- _type] .type .type, val, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, st[r0 -- _type] .type .type, val, str)]]