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Proof step 54 from proof validrefs-trans-01 (previous step)

is_obj(str, r, st), validrefs(str, (st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0) .last ' + refs1, ty0, st), st[r -- _type] .type ≤ ty, mkfs(class, ty3, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty3, fieldvar) ']), validrefs(str, st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0, ty3, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0, ty1, st0) ∧ validrefs(str0, (st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0) .last ' + refs, ty2, st0) → validrefs(str0, (st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0) + refs, ty1, st0) ⊦ r = jvmref, validrefs(str, r ' + (st[r -- mkfs(class, ty3, fieldvar) '] .refval ' + refs0) + refs1, ty, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 53:
st[r -- mkfs(class, ty3, fieldvar) '] = refval(r0), is_obj(str, r, st), validrefs(str, (r0 ' + refs0) .last ' + refs1, ty0, st), st[r -- _type] .type ≤ ty, mkfs(class, ty3, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty3, fieldvar) ']), validrefs(str, r0 ' + refs0, ty3, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, (r0 ' + refs0) .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ r = jvmref, validrefs(str, r ' + (r0 ' + refs0) + refs1, ty, st)

Rule argument

[speclemmaarg: ,is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) ,[val, r] → [st[r -- mkfs(class, ty3, fieldvar) '], r0] ,T ,javavalue , ,elim-13 ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty3, fieldvar) '], r0)]]