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Proof step 42 from proof validrefs-delcycle (previous step)

refs1 .last = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), is_obj(str, r0, st) ∨ is_array(str, r0, st), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

User applied rule case distinction

And obtained the following new goals

Proof step 28:
is_obj(str, r0, st), refs1 .last = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)
Proof step 41:
is_array(str, r0, st), refs1 .last = jvmref, validrefs(str, (r0 ' + acc) + r ' + refs0 + r ' + refs1, ty, st), st[r0 -- _type] .type ≤ ty, ∀ str, r, refs0, refs1, ty, st. validrefs(str, acc + r ' + refs0 + r ' + refs1, ty, st) ∧ refs1 ≠ [] ∧ refs1 .last = jvmref → validrefs(str, acc + r ' + refs1, ty, st) ⊦ r0 = jvmref, refs1 = [], validrefs(str, (r0 ' + acc) + r ' + refs1, ty, st)

Rule argument

[CASEDARG : pos: left 3, ()]

Additional information

[[CONCRETESIMPRULES : ()]]