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Proof step 40 from proof junkrefs-put-norefval-01 (previous step)

is_array(str, r, st), junkrefs(str, r ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(val, ty0), st[r -- _type] .type ≤ ty, ∀ val, ty0, str, ty, st, r1, class, fieldvar. okval(val, ty0) ∧ junkrefs(str, acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) → ty0 = void_type ∨ mkfs(class, ty0, fieldvar) ' = _length ∨ is_referencevalue(val) ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, junkrefs(str, r ' + acc, ty, st), is_referencevalue(val)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ 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 28:
¬ (is_array(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- _type]) .type ≤ ty), is_array(str, r, st), junkrefs(str, r ' + acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(val, ty0), st[r -- _type] .type ≤ ty, ∀ val, ty0, str, ty, st, r1, class, fieldvar. okval(val, ty0) ∧ junkrefs(str, acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) → ty0 = void_type ∨ mkfs(class, ty0, fieldvar) ' = _length ∨ is_referencevalue(val) ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, junkrefs(str, r ' + acc, ty, st), is_referencevalue(val)
Proof step 39:
is_array(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) ∧ (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- _length]) .intval ∧ is_referencevalue(st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- i ']) ∧ acc .first = (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- i ']) .refval ∧ junkrefs(str, acc, (st[r1 -- mkfs(class, ty0, fieldvar) ', val][r -- _type]) .type .type, st[r1 -- mkfs(class, ty0, fieldvar) ', val])), okval(val, ty0), st[r -- _type] .type ≤ ty, ∀ val, ty0, str, ty, st, r1, class, fieldvar. okval(val, ty0) ∧ junkrefs(str, acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) → ty0 = void_type ∨ mkfs(class, ty0, fieldvar) ' = _length ∨ is_referencevalue(val) ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, junkrefs(str, r ' + acc, ty, st), is_referencevalue(val)

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r1 -- mkfs(class, ty0, fieldvar) ', val], ty, acc, r, str)]]