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Proof step 52 from proof validstatfield-putrkvs (previous step)

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, validvals(str, rkvs1, st), validval(str, jvmref -- mkfs(class, ty, fieldvar) ', val, st), validvals(str, rkvs0, st), is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs0, (is_reftype(ty) → validrefval(str, val, ty, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', val][rkvs0])) ∧ okval(val, ty)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 19:
⊦ validval(str, r -- sk, val, st) ↔ (is_fskey(sk) → validval(str, val, sk .fs .type, st) ∧ sk .fs .type ≠ void_type ∧ sk ≠ _length) ∧ (is_indexkey(sk) → validval(str, val, st[r -- _type] .type .type, st))
Proof step 51:
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, validvals(str, rkvs1, st), ( is_fskey(mkfs(class, ty, fieldvar) ') → validval(str, val, mkfs(class, ty, fieldvar) ' .fs .type, st) ∧ mkfs(class, ty, fieldvar) ' .fs .type ≠ void_type ∧ mkfs(class, ty, fieldvar) ' ≠ _length) ∧ (is_indexkey(mkfs(class, ty, fieldvar) ') → validval(str, val, st[jvmref -- _type] .type .type, st)), validvals(str, rkvs0, st), is_reftype(ty) → validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ ty = void_type, jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs0, (is_reftype(ty) → validrefval(str, val, ty, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', val][rkvs0])) ∧ okval(val, ty)

Rule argument

[crewrite-arg: validrefkeyval-def , F , [st, val, sk, r, str] → [st, val, mkfs(class, ty, fieldvar) ', jvmref, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, val, mkfs(class, ty, fieldvar) ', jvmref, str)]]