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Proof step 73 from proof validrefs-putbar-01 (previous step)

validrefs(str, r0 ' + refs0, ty, putByteArray(bytes, r, i, st)), okbytearray(r, st), is_valid_ref(str, r0, putByteArray(bytes, r, i, st)), st[r0 -- _type] .type ≤ ty, ∀ i, bytes, ty, r0, str, st, r, refs. # refs < # refs0 → (okbytearray(r, st) ∧ validrefs(str, r0 ' + refs, ty, putByteArray(bytes, r, i, st)) → junkref(str, r0, st) ∨ validrefs(str, r0 ' + refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st), junkref(str, r0, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ 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 45:
¬ (is_obj(str, r0, putByteArray(bytes, r, i, st)) ∧ (putByteArray(bytes, r, i, st)[r0 -- _type]) .type ≤ ty), validrefs(str, r0 ' + refs0, ty, putByteArray(bytes, r, i, st)), okbytearray(r, st), is_valid_ref(str, r0, putByteArray(bytes, r, i, st)), st[r0 -- _type] .type ≤ ty, ∀ i, bytes, ty, r0, str, st, r, refs. # refs < # refs0 → (okbytearray(r, st) ∧ validrefs(str, r0 ' + refs, ty, putByteArray(bytes, r, i, st)) → junkref(str, r0, st) ∨ validrefs(str, r0 ' + refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st), junkref(str, r0, st)
Proof step 72:
is_obj(str, r0, putByteArray(bytes, r, i, st)) ∧ (putByteArray(bytes, r, i, st)[r0 -- _type]) .type ≤ ty, refs0 = [] ∨ (∃ fs. fs ' ∈ instfields((putByteArray(bytes, r, i, st)[r0 -- _type]) .type .class) ∧ is_referencevalue(putByteArray(bytes, r, i, st)[r0 -- fs ']) ∧ refs0 .first = (putByteArray(bytes, r, i, st)[r0 -- fs ']) .refval ∧ validrefs(str, refs0, fs .type, putByteArray(bytes, r, i, st))), okbytearray(r, st), is_valid_ref(str, r0, putByteArray(bytes, r, i, st)), st[r0 -- _type] .type ≤ ty, ∀ i, bytes, ty, r0, str, st, r, refs. # refs < # refs0 → (okbytearray(r, st) ∧ validrefs(str, r0 ' + refs, ty, putByteArray(bytes, r, i, st)) → junkref(str, r0, st) ∨ validrefs(str, r0 ' + refs, ty, st)) ⊦ r0 = jvmref, validrefs(str, r0 ' + refs0, ty, st), junkref(str, r0, st)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [putByteArray(bytes, r, i, st), ty, refs0, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (putByteArray(bytes, r, i, st), ty, refs0, r0, str)]]