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Proof step 12 from proof pathex-class (previous step)

is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st) ⊦ r = (st[r -- fs '] .refval ' + refs) .last, st[r -- fs '] .refval ≠ jvmref ∧ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r -- fs '] .refval, (st[r -- fs '] .refval ' + refs) .last, st), st[r -- fs '] .refval = jvmref ∧ (st[r -- fs '] .refval ' + refs) .last = jvmref

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ r ≠ jvmref ∧ (¬ is_valid_ref(str, r, st) ∨ ¬ st[r -- _type] .type ≤ ty) → ¬ validrefs(str, r ' + refs, ty, st)
Proof step 11:
¬ (st[r -- fs '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- fs '] .refval, st) ∨ ¬ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type)), is_obj(str, r, st), fs ' ∈ instfields(st[r -- _type] .type .class), is_referencevalue(st[r -- fs ']), validrefs(str, st[r -- fs '] .refval ' + refs, fs .type, st) ⊦ r = (st[r -- fs '] .refval ' + refs) .last, st[r -- fs '] .refval ≠ jvmref ∧ st[st[r -- fs '] .refval -- _type] .type ≤ fs .type ∧ path∃(str, st[r -- fs '] .refval, (st[r -- fs '] .refval ' + refs) .last, st), st[r -- fs '] .refval = jvmref ∧ (st[r -- fs '] .refval ' + refs) .last = jvmref

Rule argument

[crewrite-arg: validrefs-is-junk , F , [st, ty, refs, r, str] → [st, fs .type, refs, st[r -- fs '] .refval, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, fs .type, refs, st[r -- fs '] .refval, str)]]