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Proof step 57 from proof validstatfield-putrkvs (previous step)

jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs, validvals(str, rkvs, st), mkfs(class, ty, fieldvar) ' ∈ statfields(class), tdname∃(str, class), initdone(class, st), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, okval(st[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, (is_reftype(ty) → validrefval(str, st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[rkvs])) ∧ okval(st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ rk ∈ rkvs ↔ (∃ rkvs0, val, rkvs1. rkvs = rkvs0 + ((rk × val) + rkvs1) ∧ ¬ rk ∈ rkvs1)
Proof step 56:
∃ rkvs0, val, rkvs1. rkvs = rkvs0 + (((jvmref -- mkfs(class, ty, fieldvar) ') × val) + rkvs1) ∧ ¬ jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs1, validvals(str, rkvs, st), mkfs(class, ty, fieldvar) ' ∈ statfields(class), tdname∃(str, class), initdone(class, st), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, okval(st[jvmref -- mkfs(class, ty, fieldvar) '], ty), type∃(str, ty), jvmref ∈ st, is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, (is_reftype(ty) → validrefval(str, st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty, st[rkvs])) ∧ okval(st[rkvs][jvmref -- mkfs(class, ty, fieldvar) '], ty)

Rule argument

[speclemmaarg: , rk ∈ rkvs ↔ (∃ rkvs0, val, rkvs1. rkvs = rkvs0 + ((rk × val) + rkvs1) ∧ ¬ rk ∈ rkvs1) ,[rkvs, rk] → [rkvs, jvmref -- mkfs(class, ty, fieldvar) '] ,F ,assoclist ,refkeyvalues ,lastoccurrence-key ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (rkvs, jvmref -- mkfs(class, ty, fieldvar) ')]]