//	3,     For any If block predecessor p, update relationship p->b.
//	4,     Traverse all successors of b.
//	5,       For any successor s of b, try to update relationship b->s, if a
//	         contradiction is found then redirect p to another successor of b.
func fuseBranchRedirect(f *Func) bool {
	ft := newFactsTable(f)
	ft.checkpoint()

	changed := false
	for i := len(f.Blocks) - 1; i >= 0; i-- {
		b := f.Blocks[i]

			// #5:  N2<=X<=N1  |  N1<=N2 | collapse path (learn that N1=X=N2)
			// #6:  N2<=X<=N1  |  N1<N2  | contradiction
			// #7:  N2<X<N1    |  N1<=N2 | contradiction in the path
			// #8:  N2<X<N1    |  N1<N2  | contradiction

			if strict {
				// Cases #6 and #8: contradiction
				return false
			}

			// We're in case #5 or #7. Try to collapse path, and that will

	// entry(x) < entry(y) allows cases x-dom-y and x-then-y.
	// But by supposition, x does not dominate y. So we have x-then-y.
	//
	// For contradiction, assume x dominates z.
	// Then entry(x) < entry(z) < exit(z) < exit(x).
	// But we know x-then-y, so entry(x) < exit(x) < entry(y) < exit(y).
	// Combining those, entry(x) < entry(z) < exit(z) < exit(x) < entry(y) < exit(y).

// efficient.
type factsTable struct {
	// unsat is true if facts contains a contradiction.
	//
	// Note that the factsTable logic is incomplete, so if unsat
	// is false, the assertions in factsTable could be satisfiable
	// *or* unsatisfiable.
	unsat      bool // true if facts contains a contradiction
	unsatDepth int  // number of unsat checkpoints

	facts map[pair]relation // current known set of relation

arrive at the idea of doing those exact calculations. Nowhere is it mentioned
that this test extends the 2-by-1 guess into a 3-by-2 guess. The proof of the
Good Guess Guarantee is only for the 2-by-1 guess and argues by contradiction,
making it difficult to understand how modifications like adding another digit
or adjusting the quotient range affects the overall bound.

All that said, Knuth remains the canonical reference. It is dense but packed

		// This tests for i <= cap, which we can only prove
		// using the derived relation between len and cap.
		// This depends on finding the contradiction, since we
		// don't query this condition directly.
		useSlice(b[:i]) // ERROR "Proved IsSliceInBounds$"
	}
}

func f18(b []int, x int, y uint) {
	_ = b[x]
	_ = b[y]

the executable.

  It may happen that this requirement contradicts the license
restrictions of other proprietary libraries that do not normally
accompany the operating system.  Such a contradiction means you cannot
use both them and the Library together in an executable that you
distribute.

  7. You may place library facilities that are a work based on the

    if (!isa<func::FuncOp, IfOp, WhileOp>(contraction->getParentOp())) {
      return rewriter.notifyMatchFailure(
          contraction,
          "fused operation must be nested inside a function, If or While");
    }

    // If the contraction is used in multiple places, fusing it will only create
    // more contraction nodes, which is slower.
    if (!contraction.getResult().hasOneUse())

#include "tensorflow/core/framework/resource_mgr.h"

namespace mlir {
namespace TF {

//===----------------------------------------------------------------------===//
// TensorFlow Contraction Fusion.
//===----------------------------------------------------------------------===//

struct ContractionFusion {
  explicit ContractionFusion(
      StringRef output_kernel, ArrayRef<int> additional_arguments = {},

        const int y_col =
            !matmul_op.getAdjY() ? shape_y.back() : *(shape_y.rbegin() + 1);

        // Checks that matrix multiply can perform a valid contraction.
        if (x_col != y_row) {
          result_shape.clear();
          return false;
        }

        result_shape.push_back(x_row);
        result_shape.push_back(y_col);
        return true;