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Proof step 9 from proof validref-putrkvs-norefval (previous step)

okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(val, ty0), r1 ∈ st ⊦ validref(str, r, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val][rkvs]) ↔ validref(str, r, ty, st[rkvs]), mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ¬ rk ∈ rkvs → (st[rk, val][rkvs]) = (st[rkvs][rk, val])
Proof step 8:
¬ r1 -- mkfs(class, ty0, fieldvar) ' ∈ rkvs, okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(val, ty0), r1 ∈ st ⊦ validref(str, r, ty, st[rkvs][r1 -- mkfs(class, ty0, fieldvar) ', val]) ↔ validref(str, r, ty, st[rkvs]), mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, is_referencevalue(val)

Rule argument

[speclemmaarg: ,¬ rk ∈ rkvs → (st[rk, val][rkvs]) = (st[rkvs][rk, val]) ,[rkvs, val, rk, st] → [rkvs, val, r1 -- mkfs(class, ty0, fieldvar) ', st] ,F ,storefuns , ,put-rkvs-switch ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ rk ∈ rkvs → (st[rk, val][rkvs]) = st[rkvs]])], [EXTRATERMS : (rkvs, val, r1 -- mkfs(class, ty0, fieldvar) ', st)]]