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Proof step 36 from proof junkrefs-put-refval (previous step)

junkrefs(str, r3 ' + refs, ty0, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), is_valid_ref(str, r1, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), st[r1 -- _type] .type ≤ ty, is_obj(r1, st), st[r3 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), ∀ str0, ty1, st0, r, r2, fs0. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ is_obj(r2, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r1 = jvmref, r3 = jvmref, _type = mkfs(class, ty0, fieldvar) ', junkrefs(str, r1 ' + r3 ' + refs, ty, st), junkref(str, r3, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ 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 35:
is_obj(str, r1, st) ∧ st[r1 -- _type] .type ≤ ty, junkrefs(str, r3 ' + refs, ty0, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), is_valid_ref(str, r1, st), is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r3)]), st[r1 -- _type] .type ≤ ty, is_obj(r1, st), st[r3 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), ∀ str0, ty1, st0, r, r2, fs0. ¬ junkrefs(str0, r3 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r, st0) ∧ is_obj(r2, st0) ∧ st0[r -- _type] .type ≤ fs0 .type ∧ r ≠ jvmref ∧ fs0 ' ∈ instfields(st0[r2 -- _type] .type .class) → ¬ junkrefs(str0, r3 ' + refs, ty1, st0[r2 -- fs0 ', refval(r)]) ⊦ r1 = jvmref, r3 = jvmref, _type = mkfs(class, ty0, fieldvar) ', r3 ' + refs ≠ [] ∧ (∃ fs. fs ' ∈ instfields(st[r1 -- _type] .type .class) ∧ is_referencevalue(st[r1 -- fs ']) ∧ (r3 ' + refs) .first = st[r1 -- fs '] .refval ∧ junkrefs(str, r3 ' + refs, fs .type, st)), junkref(str, r3, st)

Rule argument

[crewrite-arg: junkrefs-class , F , [st, ty, refs, r, str] → [st, ty, r3 ' + refs, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ ¬ is_obj(str, r, st) → ( is_valid_ref(str, r, st) ↔ is_array(str, r, st))], [CSIMPSEQ : ⊦ is_obj(r, st) → ¬ is_array(str, r, st)])], [EXTRATERMS : (st, ty, r3 ' + refs, r1, str)]]