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

newref(r, st), validrefs(str, r0 ' + acc, ty, addarray(r, ty0, vals, st)), is_obj(str, r0, addarray(r, ty0, vals, st)) ∨ is_array(str, r0, 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 case distinction

And obtained the following new goals

Proof step 19:
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)
Proof step 32:
is_array(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)

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]