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Proof step 77 from proof junkrefs-put-refval-01 (previous step)

st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), st[r0 -- _type] .type ≤ ty0, junkrefs(str, r1 ' + r2 ' + refs, ty, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]), ∀ str0, ty1, st0, r3, fs, r4. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs .type ≠ void_type ∧ fs ' ≠ _length → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r = r1, r1 = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r0 = jvmref, junkref(str, r0, st), r ≠ r2 ∧ ¬ r ∈ refs, ∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r2 = st[r1 -- i '] .refval ∧ junkrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 70:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( junkrefs(str, r ' + refs, ty, st) ↔ refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ junkrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 76:
is_array(str, r1, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, st[r1 -- _type] .type ≤ ty, is_array(str, r1, st), st[r0 -- _type] .type ≤ ty0, r2 ' + refs ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _length]) .intval ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- i ']) ∧ (r2 ' + refs) .first = (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- i ']) .refval ∧ junkrefs (str, r2 ' + refs, (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .type, st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)])), ∀ str0, ty1, st0, r3, fs, r4. ¬ junkrefs(str0, r2 ' + refs, ty1, st0) ∧ ¬ junkref(str0, r3, st0) ∧ st0[r3 -- _type] .type ≤ fs .type ∧ r3 ≠ jvmref ∧ fs .type ≠ void_type ∧ fs ' ≠ _length → ¬ junkrefs(str0, r2 ' + refs, ty1, st0[r4 -- fs ', refval(r3)]) ⊦ r = r1, r1 = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r0 = jvmref, junkref(str, r0, st), r ≠ r2 ∧ ¬ r ∈ refs, ∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ r2 = st[r1 -- i '] .refval ∧ junkrefs(str, st[r1 -- i '] .refval ' + refs, st[r1 -- _type] .type .type, st)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)], ty, r2 ' + refs, r1, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → ( is_array (str, r0, st[r -- sk, val]) ↔ is_array(str, r0, st))], [CSIMPSEQ : ⊦ ty ≠ void_type → (st[ r -- mkfs (class, ty, fieldvar) ', val] [r0 -- _type ] ) = st[r0 -- _type]])], [EXTRATERMS : (st[r -- mkfs(class, ty0, fieldvar) ', refval(r0)], ty, r2 ' + refs, r1, str)]]