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Proof step 42 from proof junkrefs-put-norefval-equiv (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 30:
⊦ 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 33:
¬ (is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty), is_array(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(val, ty0), r1 ∈ st, junkrefs(str, r ' + acc, ty, st), st[r -- _type] .type ≤ ty, ∀ st, r1, class, ty0, fieldvar, val, str, ty. okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0) ∧ r1 -- mkfs(class, ty0, fieldvar) ' ∈ st ∧ okval(val, ty0) ∧ r1 ∈ st ∧ junkrefs(str, acc, ty, st) → mkfs(class, ty0, fieldvar) ' = _length ∨ ty0 = void_type ∨ is_referencevalue(val) ∨ junkrefs(str, acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) ⊦ mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r = jvmref, is_referencevalue(val), acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st[r1 -- mkfs(class, ty0, fieldvar) ', val]))
Proof step 41:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, is_array(str, r, st[r1 -- mkfs(class, ty0, fieldvar) ', val]), okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0), r1 -- mkfs(class, ty0, fieldvar) ' ∈ st, okval(val, ty0), r1 ∈ st, acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st)), st[r -- _type] .type ≤ ty, ∀ st, r1, class, ty0, fieldvar, val, str, ty. okval(st[r1 -- mkfs(class, ty0, fieldvar) '], ty0) ∧ r1 -- mkfs(class, ty0, fieldvar) ' ∈ st ∧ okval(val, ty0) ∧ r1 ∈ st ∧ junkrefs(str, acc, ty, st) → mkfs(class, ty0, fieldvar) ' = _length ∨ ty0 = void_type ∨ is_referencevalue(val) ∨ junkrefs(str, acc, ty, st[r1 -- mkfs(class, ty0, fieldvar) ', val]) ⊦ mkfs(class, ty0, fieldvar) ' = _length, ty0 = void_type, r = jvmref, is_referencevalue(val), acc ≠ [] ∧ (∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ junkrefs(str, acc, st[r -- _type] .type .type, st[r1 -- mkfs(class, ty0, fieldvar) ', val]))

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, str)]]