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Proof step 28 from proof validrefs-trans-01 (previous step)

st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, refs0 .last ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ refs0 = [], r = jvmref, validrefs(str, r ' + (r0 ' + refs0) + refs1, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 23:
⊦ 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 27:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ ty, st[r -- i '] = refval(r0), st[r -- _type] .type ≤ ty, 0 < st[r -- _length] .intval, 0 ≤ i, validrefs(str, r0 ' + refs0, st[r -- _type] .type .type, st), i < st[r -- _length] .intval, is_array(str, r, st), validrefs(str, refs0 .last ' + refs1, ty0, st), ∀ str0, ty1, st0, refs, ty2. validrefs(str0, r0 ' + refs0, ty1, st0) ∧ validrefs(str0, refs0 .last ' + refs, ty2, st0) → validrefs(str0, (r0 ' + refs0) + refs, ty1, st0) ⊦ refs0 = [], r = jvmref, (r0 ' + refs0) + refs1 = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ ((r0 ' + refs0) + refs1) .first = st[r -- i '] .refval ∧ validrefs(str, (r0 ' + refs0) + refs1, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, (r0 ' + refs0) + refs1, r, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, (r0 ' + refs0) + refs1, r, str)]]