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With inspiration from other libraries

There is a newer version: 2.12.15

package org.hamcrest.core;

import org.hamcrest.*;

import java.util.ArrayList;

public class CombinableMatcher extends TypeSafeDiagnosingMatcher {
  private final Matcher matcher;

  public CombinableMatcher(Matcher matcher) {
    this.matcher = matcher;
  }

  @Override
  protected boolean matchesSafely(T item, Description mismatch) {
    if (!matcher.matches(item)) {
      matcher.describeMismatch(item, mismatch);
      return false;
    }
    return true;
  }

  @Override
  public void describeTo(Description description) {
    description.appendDescriptionOf(matcher);
  }

  public CombinableMatcher and(Matcher other) {
    return new CombinableMatcher(new AllOf(templatedListWith(other)));
  }

  public CombinableMatcher or(Matcher other) {
    return new CombinableMatcher(new AnyOf(templatedListWith(other)));
  }

  private ArrayList> templatedListWith(Matcher other) {
    ArrayList> matchers = new ArrayList>();
    matchers.add(matcher);
    matchers.add(other);
    return matchers;
  }

  /**
   * Creates a matcher that matches when both of the specified matchers match the examined object.
   * 
   * For example:
   * 
assertThat("fab", both(containsString("a")).and(containsString("b")))
   */
  @Factory
  public static  CombinableBothMatcher both(Matcher matcher) {
    return new CombinableBothMatcher(matcher);
  }
  
  public static final class CombinableBothMatcher {
    private final Matcher first;
    public CombinableBothMatcher(Matcher matcher) {
        this.first = matcher;
    }
    public CombinableMatcher and(Matcher other) {
      return new CombinableMatcher(first).and(other);
    }
  }

  /**
   * Creates a matcher that matches when either of the specified matchers match the examined object.
   * 
   * For example:
   * 
assertThat("fan", either(containsString("a")).and(containsString("b")))
   */
  @Factory
  public static  CombinableEitherMatcher either(Matcher matcher) {
    return new CombinableEitherMatcher(matcher);
  }
  
  public static final class CombinableEitherMatcher {
    private final Matcher first;
    public CombinableEitherMatcher(Matcher matcher) {
        this.first = matcher;
    }
    public CombinableMatcher or(Matcher other) {
      return new CombinableMatcher(first).or(other);
    }
  }
}