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

is_obj(str, r0, addarray(r, ty0, vals, st)), newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ 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 18:
is_obj(str, r0, addarray(r, ty0, vals, st)) ∧ (addarray(r, ty0, vals, st)[r0 -- _type]) .type ≤ ty, is_obj(str, r0, addarray(r, ty0, vals, st)), newref(r, st), acc = [] ∨ (∃ fs. fs ' ∈ instfields((addarray(r, ty0, vals, st)[r0 -- _type]) .type .class) ∧ is_referencevalue(addarray(r, ty0, vals, st)[r0 -- fs ']) ∧ acc .first = (addarray(r, ty0, vals, st)[r0 -- fs ']) .refval ∧ validrefs(str, acc, fs .type, addarray(r, ty0, vals, st))), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, ty0, vals, st. validrefs(str, acc, ty, addarray(r, ty0, vals, st)) ∧ newref(r, st) → r = jvmref ∨ r ∈ acc ∨ validrefs(str, acc, ty, st) ⊦ r = jvmref, r = r0, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Rule argument

[crewrite-arg: validrefs-class , F , [st, ty, refs, r, str] → [addarray(r, ty0, vals, st), ty, acc, r0, str] ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ r ≠ r0 → ( is_obj (str, r, addarray(r0, ty0, vals, st)) ↔ is_obj(str, r, st))], [CSIMPSEQ : ⊦ (refs + refs0) + refs1 = refs + refs0 + refs1], [CSIMPSEQ : ⊦ r ≠ r0 → (addarray(r, ty, vals, st) [r0 -- sk ] ) = st[r0 -- sk]])], [EXTRATERMS : (addarray(r, ty0, vals, st), ty, acc, r0, str)]]