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Proof step 55 from proof junkrefs-put-badfield (previous step)

st[r -- i '] = refval(r2), junkrefs(str, r2 ' + refs, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val]), 0 < (st[r0 -- fs ', val][r -- _length]) .intval, 0 ≤ i, i < (st[r0 -- fs ', val][r -- _length]) .intval, is_array(str, r, st), (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1, fs0, val0. junkrefs(str0, r2 ' + refs, ty0, st0[r1 -- fs0 ', val0]) → junkrefs(str0, r2 ' + refs, ty0, st0) ∨ is_typevalue(st0[r1 -- _type]) ∧ is_reftype(st0[r1 -- _type] .type), r ≠ r0 ∨ _type ≠ fs ', r ≠ r0 ∨ _length ≠ fs ' ⊦ r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 44:
⊦ rk ≠ rk0 → (st[rk0, val][rk]) = st[rk]
Proof step 54:
r -- _length ≠ r0 -- fs ', st[r -- i '] = refval(r2), junkrefs(str, r2 ' + refs, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val]), 0 < st[r -- _length] .intval, 0 ≤ i, i < st[r -- _length] .intval, is_array(str, r, st), (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str0, ty0, st0, r1, fs0, val0. junkrefs(str0, r2 ' + refs, ty0, st0[r1 -- fs0 ', val0]) → junkrefs(str0, r2 ' + refs, ty0, st0) ∨ is_typevalue(st0[r1 -- _type]) ∧ is_reftype(st0[r1 -- _type] .type), r ≠ r0 ∨ _type ≠ fs ', r ≠ r0 ∨ _length ≠ fs ' ⊦ r = jvmref, junkrefs(str, r ' + r2 ' + refs, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Rule argument

[speclemmaarg: ,rk ≠ rk0 → (st[rk0, val][rk]) = st[rk] ,[rk, val, rk0, st] → [r -- _length, val, r0 -- fs ', st] ,F ,store ,javastore-ostorea ,At-other ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r -- sk = r0 -- sk0 ↔ r = r0 ∧ sk = sk0], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ sk ≠ sk0 → (st[r -- sk, val][r0 -- sk0]) = st[r0 -- sk0]])], [EXTRATERMS : (r -- _length, val, r0 -- fs ', st)]]