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Proof step 21 from proof validrefs-levelsubset-01 (previous step)

is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str0, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) ∧ validref(str1, st[r -- mkfs(class, ty1, fieldvar) '] .refval, ty3, st0) → validrefs(str1, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, ty2, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- mkfs(class, ty1, fieldvar) '] .refval = st[r -- fs '] .refval ∧ validrefs(str, st[r -- mkfs(class, ty1, fieldvar) '] .refval ' + refs, fs .type, st)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 20:
st[r -- mkfs(class, ty1, fieldvar) '] = refval(r0), is_obj(str, r, st), is_obj(str0, r, st), level⊆(str, str0), validref(str, r, ty, st), st[r -- _type] .type ≤ ty0, st[r -- _type] .type ≤ ty, mkfs(class, ty1, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- mkfs(class, ty1, fieldvar) ']), validrefs(str0, r0 ' + refs, ty1, st), ∀ str1, str2, ty2, st0, ty3. level⊆(str1, str2) ∧ validrefs(str2, r0 ' + refs, ty2, st0) ∧ validref(str1, r0, ty3, st0) → validrefs(str1, r0 ' + refs, ty2, st0) ⊦ r = jvmref, ∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ r0 = st[r -- fs '] .refval ∧ validrefs(str, r0 ' + refs, fs .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)]]