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Proof step 49 from proof junkrefs-put-refval-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ 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 40:
¬ ( is_array(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty), is_array(str, r1, st), st[r0 -- _type] .type ≤ ty0, junkrefs(str, r1 ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]), st[r1 -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs .type ≠ void_type ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r0 = jvmref, junkref(str, r0, st), acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ acc .first = st[r1 -- i '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st))
Proof step 48:
is_array(str, r1, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type ≤ ty, is_array(str, r1, st), st[r0 -- _type] .type ≤ ty0, acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _length]) .intval ∧ is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- i ']) ∧ acc .first = (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- i ']) .refval ∧ junkrefs (str, acc, (st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)][r1 -- _type]) .type .type, st[r1 -- mkfs(class, ty0, fieldvar) ', refval(r0)])), st[r1 -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, r. ¬ junkrefs(str, acc, ty, st) ∧ ¬ junkref(str, r0, st) ∧ st[r0 -- _type] .type ≤ fs .type ∧ r0 ≠ jvmref ∧ fs .type ≠ void_type ∧ fs ' ≠ _length → ¬ junkrefs(str, acc, ty, st[r -- fs ', refval(r0)]) ⊦ r1 = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r0 = jvmref, junkref(str, r0, st), acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r1 -- _length] .intval ≤ i ∧ is_referencevalue(st[r1 -- i ']) ∧ acc .first = st[r1 -- i '] .refval ∧ junkrefs(str, acc, st[r1 -- _type] .type .type, st))

Rule argument

[crewrite-arg: junkrefs-array , 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)]]