Local Arguments update {_} {_} _ _ _ _ _ : simpl never.
Section AppliedImpliesInputProof.
Context {orig_base_params : BaseParams}.
Context {one_node_params : OneNodeParams orig_base_params}.
Context {raft_params : RaftParams orig_base_params}.
Context {oiai : output_implies_applied_interface}.

Lemma in_input_trace_or_app :
forall c id i tr1 tr2,
in_input_trace c id i tr1 \/ in_input_trace c id i tr2 ->
in_input_trace c id i (tr1 ++ tr2).