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Proof step 77 from proof junkrefs-put-refval (previous step)

st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_obj(r, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), junkrefs(str, r1 ' + r2 ' + refs, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r = r1, r1 = jvmref, r0 = jvmref, junkref(str, r0, st), r ≠ r2 ∧ ¬ r ∈ refs, ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r2 = st[r1 -- fs '] .refval ∧ junkrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ 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 76:
is_obj(str, r1, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, st[r1 -- _type] .type ≤ ty, is_obj(str, r1, st), is_obj(r, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), r2 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- fs ']) ∧ (r2 ' + refs) .first = (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- fs ']) .refval ∧ junkrefs(str, r2 ' + refs, fs .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)])), ∀ str0, ty1, st0, r3, r4, fs. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ is_obj(r4, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs ' ∈ instfields(st0[r4 -- _type] .type .class) → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r = r1, r1 = jvmref, r0 = jvmref, junkref(str, r0, st), r ≠ r2 ∧ ¬ r ∈ refs, ∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ r2 = st[r1 -- fs '] .refval ∧ junkrefs(str, st[r1 -- fs '] .refval ' + refs, fs .type, st)

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)], ty, r2 ' + refs, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r0, st[r -- sk, val]) ↔ is_obj(str, r0, st))], [CSIMPSEQ : ⊦ r ≠ r0 → (st[r0 -- sk0, val][r -- sk]) = st[r -- sk]])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)], ty, r2 ' + refs, r1, str)]]