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Proof step 65 from proof junkrefs-put-badfield (previous step)

is_array(str, r, st), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + acc, 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 35:
⊦ 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 43:
¬ (is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty), is_array(str, r, st), junkrefs(str, r ' + acc, ty, st[r0 -- fs ', val]), st[r -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + acc, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)
Proof step 64:
is_array(str, r, st[r0 -- fs ', val]) ∧ (st[r0 -- fs ', val][r -- _type]) .type ≤ ty, is_array(str, r, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (st[r0 -- fs ', val][r -- _length]) .intval ∧ is_referencevalue(st[r0 -- fs ', val][r -- i ']) ∧ acc .first = (st[r0 -- fs ', val][r -- i ']) .refval ∧ junkrefs(str, acc, (st[r0 -- fs ', val][r -- _type]) .type .type, st[r0 -- fs ', val])), st[r -- _type] .type ≤ ty, ∀ str, ty, st, r0, fs, val. junkrefs(str, acc, ty, st[r0 -- fs ', val]) → junkrefs(str, acc, ty, st) ∨ is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type) ⊦ r = jvmref, junkrefs(str, r ' + acc, ty, st), is_typevalue(st[r0 -- _type]) ∧ is_reftype(st[r0 -- _type] .type)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [st[r0 -- fs ', val], ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st[r0 -- fs ', val], ty, acc, r, str)]]