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Proof step 34 from proof pathexplus-pathex (previous step)

is_valid_ref(str, (r ' + refs) .last, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st), is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st) ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, step∃(str, (r ' + refs) .last, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ step∃(str, r, r0, st) ↔ r ≠ jvmref ∧ is_classtype(st[r -- _type] .type) ∧ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ st[r -- fs '] .refval = r0) ∨ is_arraytype(st[r -- _type] .type) ∧ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ st[r -- i '] .refval = r0)
Proof step 33:
is_valid_ref(str, (r ' + refs) .last, st), validrefs(str, (r ' + refs) .last ' + r0 ', st[(r ' + refs) .last -- _type] .type, st), is_valid_ref(str, r, st), validrefs(str, r ' + refs + r0 ', mkclasstype(`java.lang.Object' .class), st), validrefs(str, r ' + refs, mkclasstype(`java.lang.Object' .class), st) ⊦ (r ' + refs) .last = jvmref, r = jvmref, r = r0, (r ' + refs) .last ≠ jvmref ∧ is_classtype(st[(r ' + refs) .last -- _type] .type) ∧ (∃ fs. fs ' ∈ instfields(st[(r ' + refs) .last -- _type] .type .class) ∧ is_referencevalue(st[(r ' + refs) .last -- fs ']) ∧ st[(r ' + refs) .last -- fs '] .refval = r0) ∨ is_arraytype(st[(r ' + refs) .last -- _type] .type) ∧ (∃ i. 0 ≤ i ∧ i < st[(r ' + refs) .last -- _length] .intval ∧ is_referencevalue(st[(r ' + refs) .last -- i ']) ∧ st[(r ' + refs) .last -- i '] .refval = r0)

Rule argument

[crewrite-arg: step-exists-def , F , [st, r0, r, str] → [st, r0, (r ' + refs) .last, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, r0, (r ' + refs) .last, str)]]