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Proof step 49 from proof validrefs-putbar (previous step)

okbytearray(r1, st), is_obj(`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 = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ acc .first = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(`docs2store', acc, ty0, putByteArray(bytes, r1, i, st)) ⊦ r = jvmref, validrefs(`docs2store', r ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 37:
⊦ is_obj(str, r, st) ∧ st[r -- _type] .type ≤ ty → ( validrefs(str, r ' + refs, ty, st) ↔ refs = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ refs .first = st[r -- fs '] .refval ∧ validrefs(str, refs, fs .type, st)))
Proof step 40:
¬ (is_obj(`docs2store', r, st) ∧ st[r -- _type] .type ≤ ty), okbytearray(r1, st), is_obj(`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 = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ acc .first = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(`docs2store', acc, ty0, putByteArray(bytes, r1, i, st)) ⊦ r = jvmref, validrefs(`docs2store', r ' + acc, ty, st)
Proof step 48:
is_obj(`docs2store', r, st) ∧ st[r -- _type] .type ≤ ty, okbytearray(r1, st), is_obj(`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 = [] ∨ mkfs(class, ty0, fieldvar) ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- mkfs(class, ty0, fieldvar) ']) ∧ acc .first = st[r -- mkfs(class, ty0, fieldvar) '] .refval ∧ validrefs(`docs2store', acc, ty0, putByteArray(bytes, r1, i, st)) ⊦ r = jvmref, acc = [] ∨ (∃ fs. fs ' ∈ instfields(st[r -- _type] .type .class) ∧ is_referencevalue(st[r -- fs ']) ∧ acc .first = st[r -- fs '] .refval ∧ validrefs(`docs2store', acc, fs .type, st))

Rule argument

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

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (st, ty, acc, r, `docs2store')]]