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Proof step 33 from proof validstatfield-putrkvs (previous step)

validref(str, r, ty, st), validvals(str, rkvs0, st), validvals(str, rkvs1, st), jvmref ∈ st, type∃(str, ty), is_referencevalue(st[jvmref -- mkfs(class, ty, fieldvar) ']), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, initdone(class, st), tdname∃(str, class), mkfs(class, ty, fieldvar) ' ∈ statfields(class), is_reftype(ty), validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, validref(str, r, ty, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', refval(r)][rkvs0]), jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs0, validvals(str, rkvs0, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', refval(r)]), validval(str, jvmref -- mkfs(class, ty, fieldvar) ', refval(r), st[rkvs1]), validval(str, jvmref -- mkfs(class, ty, fieldvar) ', refval(r), st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ 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 32:
validref(str, r, ty, st), validvals(str, rkvs0, st), validvals(str, rkvs1, st), jvmref ∈ st, type∃(str, ty), is_referencevalue(st[jvmref -- mkfs(class, ty, fieldvar) ']), jvmref -- mkfs(class, ty, fieldvar) ' ∈ st, initdone(class, st), tdname∃(str, class), mkfs(class, ty, fieldvar) ' ∈ statfields(class), is_reftype(ty), validrefval(str, st[jvmref -- mkfs(class, ty, fieldvar) '], ty, st) ⊦ mkfs(class, ty, fieldvar) ' = _length, ty = void_type, validref(str, r, ty, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', refval(r)][rkvs0]), jvmref -- mkfs(class, ty, fieldvar) ' ∈ rkvs0, validvals(str, rkvs0, st[rkvs1][jvmref -- mkfs(class, ty, fieldvar) ', refval(r)]), validval(str, jvmref -- mkfs(class, ty, fieldvar) ', refval(r), st[rkvs1]), ( is_fskey(mkfs(class, ty, fieldvar) ') → validval(str, refval(r), 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, refval(r), st[jvmref -- _type] .type .type, st))

Rule argument

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

Additional information

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