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Proof step 18 from proof pathex-array (previous step)

is_array(str, r, st), validrefs(str, r ' + refs0, st[r -- _type] .type, st) ⊦ r = (r ' + refs0) .last, ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (r ' + refs0) .last, st) ∨ st[r -- i '] .refval = jvmref ∧ (r ' + refs0) .last = jvmref)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs .first = st[r -- i '] .refval ∧ validrefs(str, refs, st[r -- _type] .type .type, st)))
Proof step 17:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, is_array(str, r, st), refs0 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ refs0 .first = st[r -- i '] .refval ∧ validrefs(str, refs0, st[r -- _type] .type .type, st)) ⊦ r = (r ' + refs0) .last, ∃ i. ¬ i < 0 ∧ ¬ st[r -- _length] .intval ≤ i ∧ is_referencevalue(st[r -- i ']) ∧ ( st[r -- i '] .refval ≠ jvmref ∧ st[st[r -- i '] .refval -- _type] .type ≤ st[r -- _type] .type .type ∧ path∃(str, st[r -- i '] .refval, (r ' + refs0) .last, st) ∨ st[r -- i '] .refval = jvmref ∧ (r ' + refs0) .last = jvmref)

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, st[r -- _type] .type, refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ty ≤ ty])], [EXTRATERMS : (st, st[r -- _type] .type, refs0, r, str)]]