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Proof step 10 from proof validrefs-junkrefs-append (previous step)

validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2, ty1, st), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs (str, (st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2) .last ' + refs1, st[(st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2) .last -- _type] .type, st), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, refs. validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2, ty0, st0) ∧ junkrefs (str0, (st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2) .last ' + refs, st0[(st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs0 ']) ∧ st[r -- mkfs(class, ty1, fieldvar) '] .refval = st[r -- fs0 '] .refval ∧ junkrefs(str, (st[r -- fs0 '] .refval ' + refs2) + refs1, fs0 .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 9:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), validrefs(str, r0 ' + refs2, ty1, st), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, (r0 ' + refs2) .last ' + refs1, st[(r0 ' + refs2) .last -- _type] .type, st), is_obj(str, r, st), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, refs. validrefs(str0, r0 ' + refs2, ty0, st0) ∧ junkrefs(str0, (r0 ' + refs2) .last ' + refs, st0[(r0 ' + refs2) .last -- _type] .type, st0) → junkrefs(str0, (r0 ' + refs2) + refs, ty0, st0) ⊦ r = jvmref, ∃ fs0. fs0 ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs0 ']) ∧ r0 = st[r -- fs0 '] .refval ∧ junkrefs(str, (st[r -- fs0 '] .refval ' + refs2) + refs1, fs0 .type, st)

Rule argument

[x0lemmaarg: spec-name: javavalue instance-name: lemma-name: elim-13 antecedent: succedent: is_referencevalue(val) → (r = val .refval ↔ val = refval(r)) substlist: [val, r] → [st[r -- mkfs(class, ty1, fieldvar) '], r0] add preconditions?: F is rewrite lemma?: F current spec?: F rotate lemma?: T replace all?: T paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPELIM : ⊦ is_referencevalue(val) → ( r = val .refval ↔ val = refval(r))])], [EXTRATERMS : (st[r -- mkfs(class, ty1, fieldvar) '], r0)]]