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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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Eval Rules

if IsEqualAsMorphism( Precompose( tau_alpha, alpha ), Precompose( tau_beta, beta ) ) then
  Precompose( UniversalMorphismIntoFiberProduct( FiberProduct( alpha, beta ), tau_alpha, tau_beta ), ProjectionInFactor( FiberProduct( alpha, beta ), 1 ) ) -> tau_alpha

theorem1.32 := rec( Source := [ Precompose,
                                    [ UniversalMorphismIntoFiberProduct,
                                          [ FiberProduct,
                                                "alpha",
                                                "beta"
                                          ],
                                          "tau_alpha",
                                          "tau_beta"
                                    ],
                                    [ ProjectionInFactor,
                                          [ FiberProduct,
                                                "alpha",
                                                "beta"
                                          ],
                                          1
                                    ]
                              ],
                    Range := "tau_alpha",
                    Condition := [ IsEqualAsMorphism,
                                       [ Precompose,
                                             "tau_alpha",
                                             "alpha"
                                       ],
                                       [ Precompose,
                                             "tau_beta",
                                             "beta"
                                       ]
                                 ]
                  );

Immediate Rules

@Theorem
A | .

theorem1.14 := rec( Source_List := [ rec( Source := "beta,
                                          Source_predicate := IsMonomorphism,
                                          value := true ) ],
                    Range := [ ProjectionInFactor,
                                   [ FiberProduct,
                                         "alpha",
                                          "beta"
                                   ]
                                   1
                             ],
                    Range_predicate := IsMonomorphism,
                    value := true );

True Rules

theorem 1.1 := rec( Source_Filters := [ IsZero, OBJECT_FILTER ],
                    Range_Filters := [ IsInjective, OBJECT_FILTER ] );