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Proof step 4 from proof validref-class-rec-better-keep (previous step)

is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ⊦ st[r -- mkfs(class, ty0, fieldvar) '] .refval = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ ¬ validref(str, st[r -- fs '] .refval, fs .type, st)), st[st[r -- mkfs(class, ty0, fieldvar) '] .refval -- _type] .type ≤ ty0 ∧ validref(str, st[r -- mkfs(class, ty0, fieldvar) '] .refval, ty0, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
st[r -- mkfs(class, ty0, fieldvar) '] = refval(r0), is_obj(str, r, st), st[r -- _type] .type ≤ ty, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ⊦ r0 = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval ≠ jvmref ∧ (¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∨ ¬ validref(str, st[r -- fs '] .refval, fs .type, st)), st[r0 -- _type] .type ≤ ty0 ∧ validref(str, r0, ty0, 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, ty0, 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, ty0, fieldvar) '], r0)]]