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Proof step 53 from proof junkrefs-put-null (previous step)

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

User applied rule case distinction

And obtained the following new goals

Proof step 35:
is_obj(str, r0, st), junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ is_obj(r, st) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st)
Proof step 52:
is_array(str, r0, st), junkrefs(str, r0 ' + acc, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class), is_reftype(ty0), is_obj(r, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, st, r, fs. ¬ junkrefs(str, acc, ty, st) ∧ is_obj(r, st) ∧ is_reftype(fs .type) ∧ fs ' ∈ instfields(st[r -- _type] .type .class) → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(jvmref)]) ⊦ r0 = jvmref, junkrefs(str, r0 ' + acc, ty, st)

Rule argument

[CASEDARG : pos: left 5, ()]

Additional information

[[CONCRETESIMPRULES : ()]]