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Proof step 14 from proof junkrefs-put-norefval-01 (previous step)

st[r -- mkfs(class1, ty3, fieldvar1) '] = refval(r2), junkrefs(str, r2 ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(val, ty0), ∀ val0, ty1, str0, ty2, st0, r0, class0, fieldvar0. okval(val0, ty1) ∧ junkrefs(str0, r2 ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) → ty1 = void_type ∨ mkfs(class0, ty1, fieldvar0) ' = _length ∨ is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty2, st0), r ≠ r1 ∨ class1 ≠ class ∨ ty3 ≠ ty0 ∨ fieldvar1 ≠ fieldvar ⊦ ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(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 ∧ junkrefs(str, refs, fs .type, st)))
Proof step 13:
is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- mkfs(class1, ty3, fieldvar1) '] = refval(r2), junkrefs(str, r2 ' + refs, ty3, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), mkfs(class1, ty3, fieldvar1) ' ∈ instfields(st[r -- _type] .type .class), is_obj(str, r, st), st[r -- _type] .type ≤ ty, is_obj(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(val, ty0), ∀ val0, ty1, str0, ty2, st0, r0, class0, fieldvar0. okval(val0, ty1) ∧ junkrefs(str0, r2 ' + refs, ty2, st0[r0 -- mkfs(class0, ty1, fieldvar0) ', val0]) → ty1 = void_type ∨ mkfs(class0, ty1, fieldvar0) ' = _length ∨ is_referencevalue(val0) ∨ junkrefs(str0, r2 ' + refs, ty2, st0), r ≠ r1 ∨ class1 ≠ class ∨ ty3 ≠ ty0 ∨ fieldvar1 ≠ fieldvar ⊦ ty0 = void_type, mkfs(class, ty0, fieldvar) ' = _length, r = jvmref, r2 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ (r2 ' + refs) .first = st[r -- fs '] .refval ∧ junkrefs(str, r2 ' + refs, fs .type, st)), is_referencevalue(val)

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st, ty, r2 ' + refs, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, r2 ' + refs, r, str)]]