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

0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st) ⊦ r = (st[r -- i '] .refval ' + refs) .last, st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (st[r -- i '] .refval ' + refs) .last, st), st[r -- i '] .refval = jvmref ∧ (st[r -- i '] .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 -- i '] .refval ≠ jvmref ∧ (¬ is_valid_ref(str, st[r -- i '] .refval, st) ∨ ¬ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type)), 0 ≤ i, 0 < st[r -- _length] .intval, is_array(str, r, st), i < st[r -- _length] .intval, is_referencevalue(st[r -- i ']), validrefs(str, st[r -- i '] .refval ' + refs, st[r -- _type] .type .type, st) ⊦ r = (st[r -- i '] .refval ' + refs) .last, st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (st[r -- i '] .refval ' + refs) .last, st), st[r -- i '] .refval = jvmref ∧ (st[r -- i '] .refval ' + refs) .last = jvmref

Rule argument

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

Additional information

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