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Proof step 23 from proof validrefs-applast-array-null (previous step)

st[r -- i '] .refval = jvmref, validrefs(str, refs + r ', ty, st), is_array(str, r, st), i < st[r -- _length] .intval, is_reftype(st[r -- _type] .type .type), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ validrefs(str, refs + r ' + jvmref ', ty, st), validrefs(str, r ' + jvmref ', st[r -- _type] .type, st)

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 22:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ st[r -- _type] .type, st[r -- i '] .refval = jvmref, validrefs(str, refs + r ', ty, st), is_array(str, r, st), i < st[r -- _length] .intval, is_reftype(st[r -- _type] .type .type), 0 ≤ i, 0 < st[r -- _length] .intval ⊦ validrefs(str, refs + r ' + jvmref ', ty, st), jvmref ' = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ jvmref ' .first = st[r -- i '] .refval ∧ validrefs(str, jvmref ', st[r -- _type] .type .type, st))

Rule argument

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

Additional information

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