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Proof step 31 from proof validrefs-putbar (previous step)

okbytearray(r1, st), is_array(`docs2store', r, putByteArray(bytes, r1, i, st)), st[r -- _type] .type ≤ ty, ∀ r1, st, ty, bytes, i. okbytearray(r1, st) ∧ validrefs(`docs2store', acc, ty, putByteArray(bytes, r1, i, st)) → validrefs(`docs2store', acc, ty, st), acc = [] ∨ 0 ≤ i0 ∧ i0 < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i0 ']) ∧ acc .first = st[r -- i0 '] .refval ∧ validrefs(`docs2store', acc, st[r -- _type] .type .type, putByteArray(bytes, r1, i, st)) ⊦ r = r1, r = jvmref, validrefs(`docs2store', r ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ 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 30:
is_array(`docs2store', r, st) ∧ st[r -- _type] .type ≤ ty, okbytearray(r1, st), is_array(`docs2store', r, putByteArray(bytes, r1, i, st)), st[r -- _type] .type ≤ ty, ∀ r1, st, ty, bytes, i. okbytearray(r1, st) ∧ validrefs(`docs2store', acc, ty, putByteArray(bytes, r1, i, st)) → validrefs(`docs2store', acc, ty, st), acc = [] ∨ 0 ≤ i0 ∧ i0 < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i0 ']) ∧ acc .first = st[r -- i0 '] .refval ∧ validrefs(`docs2store', acc, st[r -- _type] .type .type, putByteArray(bytes, r1, i, st)) ⊦ r = r1, r = jvmref, acc = [] ∨ (∃ i. 0 ≤ i ∧ i < st[r -- _length] .intval ∧ is_referencevalue(st[r -- i ']) ∧ acc .first = st[r -- i '] .refval ∧ validrefs(`docs2store', acc, st[r -- _type] .type .type, st))

Rule argument

[crewrite-arg: validrefs-array , F , [st, ty, refs, r, str] → [st, ty, acc, r, `docs2store'] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ ¬ is_array(str, r, st) ∧ okbytearray(r1, st) → ¬ is_array (str, r, putByteArray(bytes, r1, i, st))])], [EXTRATERMS : (st, ty, acc, r, `docs2store')]]