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Proof step 33 from proof validrefs-addobj (previous step)

validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

User applied rule case distinction

And obtained the following new goals

Proof step 19:
is_obj(str, r0, st), validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)
Proof step 32:
is_array(str, r0, st), validrefs(str, r0 ' + acc, ty, addobj(r, class, fis, st)), st[r0 -- _type] .type ≤ ty, ∀ str, ty, r, class, fis, st. validrefs(str, acc, ty, addobj(r, class, fis, st)) → validrefs(str, acc, ty, st) ∨ r ∈ acc ⊦ r0 = jvmref, r = r0, r ∈ acc, validrefs(str, r0 ' + acc, ty, st)

Rule argument

[CASEDARG : pos: left 2, ()]

Additional information

[[CONCRETESIMPRULES : ()]]