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Proof step 19 from proof validrefs-primarray (previous step)

st[r -- _type] .type = mkarraytype(ty0), ty0 ≤ ty, is_primtype(ty), is_array(str, r, st) ⊦ r = jvmref, validrefs(str, r ' + refs0, mkarraytype(ty), st) ↔ r ' + refs0 = jvmref ' ∨ okarray(r, ty, st) ∧ refs0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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 18:
is_array(str, r, st) ∧ st[r -- _type] .type ≤ mkarraytype(ty), st[r -- _type] .type = mkarraytype(ty0), ty0 ≤ ty, is_primtype(ty), is_array(str, r, st) ⊦ r = jvmref, 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 ' + refs0 = jvmref ' ∨ okarray(r, ty, st) ∧ refs0 = []

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, mkarraytype(ty), refs0, r, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ mkarraytype(ty) ≤ mkarraytype(ty0) ↔ ty ≤ ty0], [CSIMPSEQ : ⊦ r ' = r0 ' + refs ↔ r = r0 ∧ refs = []], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1])], [EXTRATERMS : (st, mkarraytype(ty), refs0, r, str)]]