∀ (cache : Std.HashMap UInt64 Lean.Expr) (varDecls : Std.HashMap Int.Linear.Var Lean.Expr)
  (polyDecls : Std.HashMap Int.Linear.Poly Lean.Expr) (exprDecls : Std.HashMap Int.Linear.Expr Lean.Expr)
  (varDecls' : Std.HashMap Int.Linear.Var Lean.Expr) (polyDecls' : Std.HashMap Int.Linear.Poly Lean.Expr)
  (exprDecls' : Std.HashMap Int.Linear.Expr Lean.Expr) (ringPolyDecls : Std.HashMap Lean.Grind.CommRing.Poly Lean.Expr)
  (ringExprDecls : Std.HashMap Lean.Meta.Grind.Arith.CommRing.RingExpr Lean.Expr)
  (cache_1 : Std.HashMap UInt64 Lean.Expr) (varDecls_1 : Std.HashMap Int.Linear.Var Lean.Expr)
  (polyDecls_1 : Std.HashMap Int.Linear.Poly Lean.Expr) (exprDecls_1 : Std.HashMap Int.Linear.Expr Lean.Expr)
  (varDecls'_1 : Std.HashMap Int.Linear.Var Lean.Expr) (polyDecls'_1 : Std.HashMap Int.Linear.Poly Lean.Expr)
  (exprDecls'_1 : Std.HashMap Int.Linear.Expr Lean.Expr)
  (ringPolyDecls_1 : Std.HashMap Lean.Grind.CommRing.Poly Lean.Expr)
  (ringExprDecls_1 : Std.HashMap Lean.Meta.Grind.Arith.CommRing.RingExpr Lean.Expr),
  ({ cache := cache, varDecls := varDecls, polyDecls := polyDecls, exprDecls := exprDecls, varDecls' := varDecls',
        polyDecls' := polyDecls', exprDecls' := exprDecls', ringPolyDecls := ringPolyDecls,
        ringExprDecls := ringExprDecls } =
      { cache := cache_1, varDecls := varDecls_1, polyDecls := polyDecls_1, exprDecls := exprDecls_1,
        varDecls' := varDecls'_1, polyDecls' := polyDecls'_1, exprDecls' := exprDecls'_1,
        ringPolyDecls := ringPolyDecls_1, ringExprDecls := ringExprDecls_1 }) =
    (cache = cache_1 ∧
      varDecls = varDecls_1 ∧
        polyDecls = polyDecls_1 ∧
          exprDecls = exprDecls_1 ∧
            varDecls' = varDecls'_1 ∧
              polyDecls' = polyDecls'_1 ∧
                exprDecls' = exprDecls'_1 ∧ ringPolyDecls = ringPolyDecls_1 ∧ ringExprDecls = ringExprDecls_1)