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Proof step 139 from proof pseq-sym-01 (previous step)

st1[r1 -- i '] = refval(jvmref), st[r -- _type] = st1[r1 -- _type], st[r -- _length] .intval = st1[r1 -- _length] .intval, is_reftype(st1[r1 -- _type] .type .type), ps=(st[r -- i '] .refval, st, jvmref, st1), i < st1[r1 -- _length] .intval, is_arraytype(st1[r1 -- _type] .type), 0 ≤ i, 0 < st1[r1 -- _length] .intval, is_array(str, r1, st1), is_array(str, r, st), ∀ i. ¬ i < 0 ∧ ¬ st1[r1 -- _length] .intval ≤ i ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i '], ∀ st, r, st0, r0, str0. maxpath(str0, r0, st0) < maxpath(str, r1, st1) → ( true → ( ¬ cyclic(str0, r, st) ∧ ¬ cyclic(str0, r0, st0) ∧ ¬ junkref(str0, r, st) ∧ ¬ junkref(str0, r0, st0) → (ps=(r, st, r0, st0) → ps=(r0, st0, r, st)))) ⊦ r1 = jvmref, r = jvmref, ps=(jvmref, st1, st[r -- i '] .refval, st), cyclic(str, r, st), cyclic(str, r1, st1), junkref(str, r, st), ¬ cyclic(str, st[r -- i '] .refval, st) ∧ ¬ junkref(str, st[r -- i '] .refval, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 137:
⊦ ps=(r, st, r1, st1) ↔ r = jvmref ∧ r1 = jvmref ∨ r ≠ jvmref ∧ r1 ≠ jvmref ∧ st[r -- _type] = st1[r1 -- _type] ∧ ( is_classtype(st[r -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1)) ∧ (∀ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '])) ∧ ( is_arraytype(st[r -- _type] .type) → st[r -- _length] .intval = st1[r1 -- _length] .intval ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) → ps=(st[r -- i '] .refval, st, st1[r1 -- i '] .refval, st1)) ∧ (∀ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ ¬ is_referencevalue(st[r -- i ']) → st[r -- i '] = st1[r1 -- i ']))
Proof step 138:
⊦ ps=(jvmref, st, jvmref, st0)

Rule argument

[crewrite-arg: pseq-def , F , [st1, r1, st, r] → [st1, jvmref, st, st[r -- i '] .refval] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, jvmref, st, st[r -- i '] .refval)]]