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Proof step 46 from proof junkrefs-addarray (previous step)

is_array(str, r, st), junkrefs(str, r ' + acc, ty, addarray(r0, ty0, vals, st)), newref(r0, st), st[r -- _type] .type ≤ ty, ∀ str, ty, r0, ty0, vals, st. junkrefs(str, acc, ty, addarray(r0, ty0, vals, st)) ∧ newref(r0, st) → r0 = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, r0 = jvmref, junkrefs(str, r ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 27:
⊦ 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 31:
¬ (is_array(str, r, addarray(r0, ty0, vals, st)) ∧ (addarray(r0, ty0, vals, st)[r -- _type]) .type ≤ ty), is_array(str, r, st), junkrefs(str, r ' + acc, ty, addarray(r0, ty0, vals, st)), newref(r0, st), st[r -- _type] .type ≤ ty, ∀ str, ty, r0, ty0, vals, st. junkrefs(str, acc, ty, addarray(r0, ty0, vals, st)) ∧ newref(r0, st) → r0 = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, r0 = jvmref, junkrefs(str, r ' + acc, ty, st)
Proof step 45:
is_array(str, r, addarray(r0, ty0, vals, st)) ∧ (addarray(r0, ty0, vals, st)[r -- _type]) .type ≤ ty, is_array(str, r, st), acc ≠ [] ∧ (∃ i. 0 ≤ i ∧ i < (addarray(r0, ty0, vals, st)[r -- _length]) .intval ∧ is_referencevalue(addarray(r0, ty0, vals, st)[r -- i ']) ∧ acc .first = (addarray(r0, ty0, vals, st)[r -- i ']) .refval ∧ junkrefs(str, acc, (addarray(r0, ty0, vals, st)[r -- _type]) .type .type, addarray(r0, ty0, vals, st))), newref(r0, st), st[r -- _type] .type ≤ ty, ∀ str, ty, r0, ty0, vals, st. junkrefs(str, acc, ty, addarray(r0, ty0, vals, st)) ∧ newref(r0, st) → r0 = jvmref ∨ junkrefs(str, acc, ty, st) ⊦ r = jvmref, r0 = jvmref, junkrefs(str, r ' + acc, ty, st)

Rule argument

[crewrite-arg: junkrefs-array , F , [st, ty, refs, r, str] → [addarray(r0, ty0, vals, st), ty, acc, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (addarray(r0, ty0, vals, st), ty, acc, r, str)]]