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Proof step 94 from proof pseq-sym-01 (previous step)

st[r -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), st[r -- fs0 '] = refval(r2), ps=(r2, st, jvmref, st1), fs0 ' ∈ instfields(class), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ 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)))) ⊦ st1[r1 -- fs0 '] = refval(r2), r = jvmref, r1 = jvmref, is_referencevalue(st1[r1 -- fs0 ']), junkref(str, r1, st1), junkref(str, r, st), cyclic(str, r1, st1), cyclic(str, r, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
⊦ 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 93:
st[r -- _type] = st1[r1 -- _type], st1[r1 -- _type] .type = mkclasstype(class), st[r -- fs0 '] = refval(r2), r2 = jvmref ∧ jvmref = jvmref ∨ r2 ≠ jvmref ∧ jvmref ≠ jvmref ∧ st[r2 -- _type] = st1[jvmref -- _type] ∧ ( is_classtype(st[r2 -- _type] .type) → (∀ fs. fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ is_referencevalue(st[r2 -- fs ']) → ps=(st[r2 -- fs '] .refval, st, st1[jvmref -- fs '] .refval, st1)) ∧ (∀ fs. fs ' ∈ instfields(st[r2 -- _type] .type .class) ∧ ¬ is_referencevalue(st[r2 -- fs ']) → st[r2 -- fs '] = st1[jvmref -- fs '])) ∧ ( is_arraytype(st[r2 -- _type] .type) → st[r2 -- _length] .intval = st1[jvmref -- _length] .intval ∧ (∀ i. 0 ≤ i ∧ i < st[r2 -- _length] .intval ∧ is_referencevalue(st[r2 -- i ']) → ps=(st[r2 -- i '] .refval, st, st1[jvmref -- i '] .refval, st1)) ∧ (∀ i. 0 ≤ i ∧ i < st[r2 -- _length] .intval ∧ ¬ is_referencevalue(st[r2 -- i ']) → st[r2 -- i '] = st1[jvmref -- i '])), fs0 ' ∈ instfields(class), ∀ fs. fs ' ∈ instfields(class) ∧ is_referencevalue(st[r -- fs ']) → ps=(st[r -- fs '] .refval, st, st1[r1 -- fs '] .refval, st1), ∀ fs. fs ' ∈ instfields(class) ∧ ¬ is_referencevalue(st[r -- fs ']) → st[r -- fs '] = st1[r1 -- fs '], ∀ 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)))) ⊦ st1[r1 -- fs0 '] = refval(r2), r = jvmref, r1 = jvmref, is_referencevalue(st1[r1 -- fs0 ']), junkref(str, r1, st1), junkref(str, r, st), cyclic(str, r1, st1), cyclic(str, r, st)

Rule argument

[crewrite-arg: pseq-def, F, [st1, r1, st, r] → [st1, jvmref, st, r2]]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st1, jvmref, st, r2)]]