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Proof step 64 from proof junkrefs-put-refval (previous step)

is_obj(r1, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r1 ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, ty, st, r0, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ is_obj(r, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 = jvmref, r0 = jvmref, junkref(str, r0, st), junkrefs(str, r1 ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 11:
¬ (is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty), is_obj(r1, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), junkrefs(str, r1 ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, ty, st, r0, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ is_obj(r, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 = jvmref, r0 = jvmref, junkref(str, r0, st), junkrefs(str, r1 ' + acc, ty, st)
Proof step 63:
is_obj(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, is_obj(r1, st), st[r0 -- _type] .type ≤ ty0, mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r1 -- _type] .type .class), acc ≠ [] ∧ (∃ fs. fs ' ∈ instfields((st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .class) ∧ is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- fs ']) ∧ acc .first = (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- fs ']) .refval ∧ junkrefs(str, acc, fs .type, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)])), is_valid_ref(str, r1, st), st[r1 -- _type] .type ≤ ty, ∀ str, ty, st, r0, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ is_obj(r, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 = jvmref, r0 = jvmref, junkref(str, r0, st), junkrefs(str, r1 ' + acc, ty, st)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)], ty, acc, r1, str)]]