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Proof step 51 from proof junkrefs-put-null (previous step)

is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- i ']) ∧ acc .first = (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- i ']) .refval ∧ junkrefs (str, acc, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, 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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 50:
acc .first = st[r0 -- i '] .refval, junkrefs (str, acc, (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type .type, 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, is_array(str, r0, st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)]), (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _type]) .type ≤ ty, is_array(str, r0, st), i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, is_referencevalue(st[r0 -- i ']), 0 ≤ i, 0 < (st[r -- mkfs(class, ty0, fieldvar) ', refval(jvmref)][r0 -- _length]) .intval, ∀ 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, acc = [], junkrefs(str, r0 ' + acc, ty, st)

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ([CSIMPFORWARD : ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j], [CSIMPFORWARD : ⊦ i < j ∧ 0 ≤ i → 0 < j], [CSIMPSEQ : ⊦ (st[r0 -- fs ', val][r -- i ']) = st[r -- i ']])]]