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Proof step 18 from proof validrefs-addarray (previous step)

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)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
newref(r, st), st[r0 -- _type] .type ≤ ty, is_obj(str, r0, st), ∀ 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), acc = [] ∨ fs ' ∈ instfields(st[r0 -- _type] .type .class) ∧ is_referencevalue(st[r0 -- fs ']) ∧ acc .first = st[r0 -- fs '] .refval ∧ validrefs(str, acc, fs .type, addarray(r, ty0, vals, st)) ⊦ r = jvmref, r = r0, r0 = jvmref, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Rule argument

[emptyarg]

Additional information

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