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(** * Common Subexpression Elimination for PHOAS Syntax *)
Require Import Coq.Lists.List.
Require Import Crypto.Compilers.Syntax.
Require Import Crypto.Compilers.Wf.
Require Import Crypto.Compilers.Z.Syntax.
Require Import Crypto.Compilers.CommonSubexpressionEliminationInterp.
Require Import Crypto.Compilers.Z.CommonSubexpressionElimination.
Lemma InterpCSE_gen inline_symbolic_expr_in_lookup t (e : Expr t) prefix
(Hwf : Wf e)
: forall x, Interp (@CSE_gen inline_symbolic_expr_in_lookup t e prefix) x = Interp e x.
Proof.
apply InterpCSE;
auto using internal_base_type_dec_bl, internal_base_type_dec_lb, internal_symbolic_op_dec_bl, internal_symbolic_op_dec_lb, denote_symbolic_op.
Qed.
Lemma InterpCSE inline_symbolic_expr_in_lookup t (e : Expr t) (Hwf : Wf e)
: forall x, Interp (@CSE inline_symbolic_expr_in_lookup t e) x = Interp e x.
Proof.
apply InterpCSE_gen; auto.
Qed.
Hint Rewrite @InterpCSE using solve_wf_side_condition : reflective_interp.
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