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

is_obj(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, class, fis. validrefs(str, acc, ty, st) → r ∈ acc ∨ validrefs(str, acc, ty, addobj(r, class, fis, st)), 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, st) ⊦ r0 = jvmref, r = r0, validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), r ∈ acc

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

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r, addobj(r0, class, fis, st)) ↔ is_obj(str, r, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (addobj(r, class1, fis, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (addobj(r, class, fis, st), ty, acc, r0, str)]]