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Proof step 15 from proof validrefs-addobj (previous step)

is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc, acc = [] ∨ mkfs(class0, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class0, ty0, fieldvar) ']) ∧ acc .first = st[r0 -- mkfs(class0, ty0, fieldvar) '] .refval ∧ validrefs(str, acc, ty0, addobj(r, class, fis, st)) ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 14:
is_obj(str, r0, st) ∧ st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc, acc = [] ∨ mkfs(class0, ty0, fieldvar) ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- mkfs(class0, ty0, fieldvar) ']) ∧ acc .first = st[r0 -- mkfs(class0, ty0, fieldvar) '] .refval ∧ validrefs(str, acc, ty0, addobj(r, class, fis, st)) ⊦ r0 = jvmref, r = r0, r ∈ acc, acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ acc .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, st))

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [st, ty, acc, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r0, str)]]