Issue 438 (#10085)

Co-authored-by: Copilot <223556219+Copilot@users.noreply.github.com>
Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>

src/tactic/bv/CMakeLists.txt

@@ -18,6 +18,7 @@ z3_add_component(bv_tactics
     bv1_blaster_tactic.h
     bv_bound_chk_tactic.h
     bv_bounds_tactic.h
+    bv_divrem_bounds_tactic.h
     bv_size_reduction_tactic.h
     bv_slice_tactic.h
     bvarray2uf_tactic.h

src/tactic/bv/bv_divrem_bounds_tactic.h

@@ -0,0 +1,63 @@
+/*++
+Copyright (c) 2026 Microsoft Corporation
+
+Module Name:
+
+    bv_divrem_bounds_tactic.h
+
+Abstract:
+
+    Tactic wrapper around the bv::divrem_bounds simplifier. It adds range
+    lemmas for bit-vector division and remainder terms with a non-constant
+    divisor. See ast/simplifiers/bv_divrem_bounds.h for details.
+
+Author:
+
+    Nikolaj Bjorner (nbjorner)
+
+Tactic Documentation
+
+## Tactic bv-divrem-bounds
+
+### Short Description
+
+Add range lemmas for bit-vector division/remainder terms with a symbolic divisor.
+
+### Long Description
+
+For a divisor `b` that is not a numeral, the remainder magnitude is bounded by
+the divisor magnitude and the unsigned quotient is bounded by the dividend.
+These facts are hidden once a division circuit is bit-blasted, so the tactic
+emits them as implied lemmas up front, letting a downstream SAT solver reason
+about magnitudes without unfolding the circuit.
+
+### Example
+
+```z3
+(declare-const a (_ BitVec 8))
+(declare-const b (_ BitVec 8))
+(declare-const c (_ BitVec 8))
+(assert (= (bvsrem a (bvadd b c)) #x05))
+(apply bv-divrem-bounds)
+```
+
+--*/
+#pragma once
+
+#include "util/params.h"
+#include "tactic/tactic.h"
+#include "tactic/dependent_expr_state_tactic.h"
+#include "ast/simplifiers/bv_divrem_bounds.h"
+
+class ast_manager;
+class tactic;
+
+inline tactic* mk_bv_divrem_bounds_tactic(ast_manager& m, params_ref const& p = params_ref()) {
+    return alloc(dependent_expr_state_tactic, m, p,
+                 [](auto& m, auto& p, auto& s) -> dependent_expr_simplifier* { return alloc(bv::divrem_bounds, m, s); });
+}
+
+/*
+  ADD_TACTIC("bv-divrem-bounds", "add range lemmas for bit-vector division/remainder terms with a symbolic divisor.", "mk_bv_divrem_bounds_tactic(m, p)")
+  ADD_SIMPLIFIER("bv-divrem-bounds", "add range lemmas for bit-vector division/remainder terms with a symbolic divisor.", "alloc(bv::divrem_bounds, m, s)")
+*/

src/tactic/smtlogics/qfaufbv_tactic.cpp

@@ -23,6 +23,7 @@ Notes:
 #include "tactic/core/elim_uncnstr_tactic.h"
 #include "tactic/bv/max_bv_sharing_tactic.h"
 #include "tactic/bv/bv_size_reduction_tactic.h"
+#include "tactic/bv/bv_divrem_bounds_tactic.h"
 #include "tactic/core/ctx_simplify_tactic.h"
 #include "tactic/smtlogics/qfbv_tactic.h"
 #include "tactic/smtlogics/smt_tactic.h"
@@ -42,6 +43,7 @@ static tactic * mk_qfaufbv_preamble(ast_manager & m, params_ref const & p) {
                     mk_propagate_values_tactic(m),
                     mk_solve_eqs_tactic(m),
                     mk_elim_uncnstr_tactic(m),
+                    mk_bv_divrem_bounds_tactic(m),
                     // sound to use? if_no_proofs(if_no_unsat_cores(mk_reduce_args_tactic(m))),
                     if_no_proofs(if_no_unsat_cores(mk_bv_size_reduction_tactic(m))),
                     using_params(mk_simplify_tactic(m), simp2_p),

src/tactic/smtlogics/qfbv_tactic.cpp

@@ -25,6 +25,7 @@ Notes:
 #include "tactic/bv/bv1_blaster_tactic.h"
 #include "tactic/bv/max_bv_sharing_tactic.h"
 #include "tactic/bv/bv_size_reduction_tactic.h"
+#include "tactic/bv/bv_divrem_bounds_tactic.h"
 #include "tactic/aig/aig_tactic.h"
 #include "sat/tactic/sat_tactic.h"
 #include "sat/sat_solver/inc_sat_solver.h"
@@ -63,6 +64,7 @@ static tactic * mk_qfbv_preamble(ast_manager& m, params_ref const& p) {
             using_params(mk_propagate_values_tactic(m), flat_and_or_p),
             using_params(mk_solve_eqs_tactic(m), solve_eq_p),
             mk_elim_uncnstr_tactic(m),
+            mk_bv_divrem_bounds_tactic(m),
             if_no_proofs(if_no_unsat_cores(mk_bv_size_reduction_tactic(m))),
             using_params(mk_simplify_tactic(m), simp2_p),