Document:

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                                                                   EXHIBIT 4.12

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                         REGISTRATION RIGHTS AGREEMENT

                         DATED AS OF FEBRUARY 10, 2000

                                    BETWEEN

                           LIBERTY MEDIA CORPORATION

                                      AND

                           SALOMON SMITH BARNEY INC.

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                         REGISTRATION RIGHTS AGREEMENT

         This Registration Rights Agreement (the "Agreement") is made and
entered into this 10th day of February, 2000, between Liberty Media
Corporation, a Delaware corporation (the "Company"), and Salomon Smith Barney
Inc. (the "Initial Purchaser").

         This Agreement is made pursuant to the Purchase Agreement, dated
February 3, 2000, between the Company and the Initial Purchaser (the "Purchase
Agreement"), which provides for the sale by the Company to the Initial
Purchaser of an aggregate of $750,000,000 original principal amount of the
Company's 3-3/4% Senior Exchangeable Debentures due 2030 (the "Debentures") (or
$1,000,000,000 aggregate original principal amount of such Debentures if the
Initial Purchaser's overallotment option is exercised in full). In order to
induce the Initial Purchaser to enter into the Purchase Agreement, the Company
has agreed to provide to the Initial Purchaser and its direct and indirect
transferees the registration rights set forth in this Agreement. The execution
of this Agreement is a condition to the closing under the Purchase Agreement.

         In consideration of the foregoing, the parties hereto agree as
follows:

         1.       Definitions.

         As used in this Agreement, the following capitalized defined terms
shall have the following meanings:

         "1933 Act" shall mean the Securities Act of 1933, as amended from time
to time.

         "1934 Act" shall mean the Securities Exchange Act of 1934, as amended
from time to time.

         "beneficial owner" shall mean (i), in the case of a Debenture held in
certificated form, the Holder of such Debenture and (ii), in the case of a
Debenture held through the Depositary, the Person identified in the records of
the Depositary's direct or indirect participants as the owner of such
Debenture; provided, however, that in the case of a beneficial owner described
in clause (ii), such beneficial owner is identified to the Company.

         "Business Day" shall mean a day that is not a Saturday, a Sunday, or a
day on which banking institutions in New York, New York are authorized or
required to be closed.

         "Closing Date" shall mean the Closing Time as defined in the Purchase
Agreement.

         "Company" shall have the meaning set forth in the preamble and shall
also include the Company's successors.

         "Debentures" shall have the meaning set forth in the second paragraph
of this Agreement.

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         "Depositary" shall mean The Depository Trust Company, or any other
depositary appointed by the Company, provided, however, that such depositary
must have an address in the Borough of Manhattan, in The City of New York.

         "Holder" shall mean the Initial Purchaser, for so long as it owns any
Debentures, and each of its successors, assigns and direct and indirect
transferees who become beneficial owners of Debentures under the Indenture.

         "Indenture" shall mean the Indenture relating to the Debentures, dated
as of July 7, 1999, between the Company and The Bank of New York, as trustee,
as supplemented by the Fourth Supplemental Indenture, dated as of February 10,
2000, between the Company and The Bank of New York, as trustee, as the same may
be amended, supplemented, waived or otherwise modified from time to time in
accordance with the terms thereof.

         "Initial Purchaser" shall have the meaning set forth in the preamble.

         "Majority Holders" shall mean the Holders of a majority of the
aggregate principal amount of Outstanding (as defined in the Indenture)
Debentures; provided that whenever the consent or approval of Holders of a
specified percentage of Debentures is required hereunder, Debentures held by
the Company and other obligors on the Debentures or any Affiliate (as defined
in the Indenture) of the Company shall be disregarded in determining whether
such consent or approval was given by the Holders of such required percentage
amount.

         "Person" shall mean an individual, partnership (general or limited),
corporation, limited liability company, trust or unincorporated organization,
or a government or agency or political subdivision thereof.

         "Prospectus" shall mean the prospectus included in the Shelf
Registration Statement, including any preliminary prospectus, and any such
prospectus as amended or supplemented by any prospectus supplement, including
any such prospectus supplement with respect to the terms of the offering of any
portion of the Debentures covered by the Shelf Registration Statement, and by
all other amendments and supplements to a prospectus, including post-effective
amendments, and in each case including all material incorporated by reference
therein.

         "Purchase Agreement" shall have the meaning set forth in the preamble.

         "Registration Expenses" shall mean any and all expenses incident to
performance of or compliance by the Company with this Agreement, including
without limitation: (i) all SEC, stock exchange or National Association of
Securities Dealers, Inc. (the "NASD") registration and filing fees, including,
if applicable, the fees and expenses of any "qualified independent underwriter"
(and its counsel) that is required to be retained by any holder of Debentures
in accordance with the rules and regulations of the NASD, (ii) all fees and
expenses incurred in connection with compliance with state securities or blue
sky laws and compliance with the rules of the NASD (including reasonable fees
and disbursements of counsel for any underwriters or Holders in connection with
blue sky qualification of any of the Debentures and any filings with

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the NASD), (iii) all expenses of any Persons in preparing or assisting in
preparing, word processing, printing and distributing any Shelf Registration
Statement, any Prospectus, any amendments or supplements thereto, any
underwriting agreements, securities sales agreements and other documents
relating to the performance of and compliance with this Agreement, (iv) all
fees and expenses incurred in connection with the listing, if any, of any of
the Debentures on any securities exchange or exchanges, (v) all rating agency
fees, (vi) the fees and disbursements of counsel for the Company and of the
independent public accountants of the Company, including the expenses of any
special audits or "cold comfort" letters required by or incident to such
performance and compliance, (vii) the fees and expenses of the Trustee, and any
escrow agent or custodian, (viii) the reasonable fees and disbursements of
Brown & Wood LLP, counsel representing the Holders of Debentures in connection
with preparing and filing the initial Shelf Registration Statement or any
amendments or supplements thereto, but not in connection with any underwritten
offering under the Shelf Registration Statement, and (ix) the reasonable fees
and disbursements of the underwriters customarily required to be paid by
issuers of securities in connection with secondary offerings of securities and
the fees and expenses of any special experts retained by the Company in
connection with any Shelf Registration Statement, but excluding underwriting
discounts and commissions and transfer taxes, if any, relating to the sale or
disposition of Debentures by a Holder.

         "SEC" shall mean the Securities and Exchange Commission or any
successor agency or government body performing the functions currently
performed by the United States Securities and Exchange Commission.

         "Shelf Registration" shall mean a registration effected pursuant to
Section 2.1 hereof.

         "Shelf Registration Statement" shall mean a "shelf" registration
statement of the Company pursuant to the provisions of Section 2.1 of this
Agreement, which covers the resale of all of the Debentures, and all amendments
to such registration statement, including post-effective amendments, in each
case including the Prospectus contained therein, all exhibits thereto and all
material incorporated by reference therein.

         "Special Counsel" shall have the meaning set forth in Section 3(f).

         "Trustee" shall mean the trustee with respect to the Debentures under
the Indenture.

         2.       Registration Under the 1933 Act.

         2.1      Shelf Registration. The Company shall, for the benefit of the
beneficial owners, at the Company's cost, (A) prepare and, as soon as
practicable but not later than 90 days following the Closing Date, file with
the SEC a Shelf Registration Statement on an appropriate form under the 1933
Act covering resales of the Debentures, (B) use its reasonable best efforts to
cause the Shelf Registration Statement to be declared effective under the 1933
Act within 180 days of the Closing Date, (C) use its reasonable best efforts to
keep the Shelf Registration Statement continuously effective in order to permit
the Prospectus forming part thereof to be usable by the beneficial owners for a
period of two years from the original issue of the

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Debentures, or for such shorter period that will terminate when all Debentures
covered by the Shelf Registration Statement have been sold pursuant to the
Shelf Registration Statement, exchanged or redeemed in accordance with their
terms or otherwise cease to be outstanding or become saleable pursuant to Rule
144(k) under the 1933 Act (the "Effectiveness Period"); provided, however, that
the Effectiveness Period in respect of the Shelf Registration Statement shall
be extended up to a maximum of 90 days if necessary to permit dealers to comply
with the applicable prospectus delivery requirements of Rule 174 under the 1933
Act and as otherwise provided herein, and (D) notwithstanding any other
provisions hereof, use its reasonable best efforts to ensure that (i) the Shelf
Registration Statement and any amendment thereto and any Prospectus forming
part thereof and any supplement thereto complies in all material respects with
the 1933 Act and the rules and regulations thereunder, (ii) the Shelf
Registration Statement and any amendment thereto does not, when it becomes
effective, contain an untrue statement of a material fact or omit to state a
material fact required to be stated therein or necessary to make the statements
therein not misleading and (iii) any Prospectus forming part of the Shelf
Registration Statement, and any supplement to such Prospectus (as amended or
supplemented from time to time), does not include an untrue statement of a
material fact or omit to state a material fact necessary in order to make the
statements, in light of the circumstances under which they were made, not
misleading.

         The Company shall not permit any securities other than Debentures to
be included in the Shelf Registration Statement. The Company further agrees, if
necessary, to supplement or amend the Shelf Registration Statement and the
Prospectus, as required by Section 3(b) below, and to furnish to the Holders of
Debentures copies of any such supplement or amendment as promptly as reasonably
practicable after filing with the SEC.

         2.2      Expenses. The Company shall pay all Registration Expenses in
connection with the registration pursuant to Section 2.1. Each beneficial owner
shall pay all underwriting expenses, discounts and commissions and transfer
taxes, if any, relating to the sale or disposition of such beneficial owner's
Debentures pursuant to the Shelf Registration Statement.

         2.3      Effectiveness. (a) The Company will be deemed not to have
used its reasonable best efforts to cause the Shelf Registration Statement to
become, or to remain, effective during the requisite period if the Company
voluntarily takes any action that would, or omits to take any action which
omission would, result in any Shelf Registration Statement not being declared
effective or in the beneficial owners of Debentures covered thereby not being
able to offer and sell such Debentures during that period as and to the extent
contemplated hereby, unless (i) such action is required by applicable law, or
(ii) such action is taken by the Company in good faith and for valid business
reasons (not including avoidance of the Company's obligations hereunder),
including the acquisition or divestiture of assets, so long as the Company
promptly thereafter complies with the requirements of Section 3(j) hereof, if
applicable.

         (b) A Shelf Registration Statement will not be deemed to have become
effective unless it has been declared effective by the SEC; provided, however,
that if, after it has been declared effective, the offering of Debentures
pursuant to a Shelf Registration Statement is

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interfered with by any stop order, injunction or other order or requirement of
the SEC or any other governmental agency or court, the Shelf Registration
Statement will be deemed not to have become effective during the period of such
interference, until the offering of Debentures pursuant to the Shelf
Registration Statement may legally resume.

         2.4      Interest. The Indenture executed in connection with the
Debentures provides that in the event that either (a) the Shelf Registration
Statement is not filed with the Commission on or prior to the 90th calendar day
following the date of original issue of the Debentures or (b) the Shelf
Registration Statement has not been declared effective on or prior to the 180th
calendar day following the date of original issue of the Debentures (each such
event referred to in clauses (a) and (b) above, a "Registration Default"), the
interest rate borne by the Debentures shall be increased ("Additional
Interest") by one quarter of one percent (0.25%) per annum upon the occurrence
of each Registration Default, which rate will increase by one quarter of one
percent at the beginning of each 90-day period (or portion thereof) that such
Additional Interest continues to accrue under any such circumstance, provided
that the maximum aggregate increase in the interest rate will in no event
exceed one percent (1%) per annum. Immediately following the cure of a
Registration Default, the accrual of Additional Interest with respect to that
particular Registration Default will cease. Immediately following the cure of
all Registration Defaults or the date on which the Debentures are saleable
pursuant to Rule 144(k) under the 1933 Act or any successor provision, the
accrual of Additional Interest will cease and the interest rate will revert to
the original rate.

         If the Shelf Registration Statement is declared effective but becomes
unusable by the Holders of Debentures covered by the Shelf Registration
Statement ("Debentures") for any reason, and the aggregate number of days in
any consecutive twelve-month period for which the Shelf Registration Statement
shall not be usable exceeds 30 days in the aggregate, then the interest rate
borne by the Debentures will be increased by 0.25% per annum of the principal
amount of the Debentures for the first 90-day period (or portion thereof)
beginning on the 31st such day that the Shelf Registration Statement ceases to
be usable, which rate shall be increased by an additional 0.25% per annum of
the principal amount of the Debentures at the beginning of each subsequent
90-day period, provided that the maximum aggregate increase in the interest
rate as a result of a Shelf Registration Statement being unusable (inclusive of
any interest that accrues on such Debentures pursuant to the first paragraph of
this Section 2.4) will in no event exceed one percent (1%) per annum. Upon the
Shelf Registration Statement once again becoming usable, the interest rate
borne by the Debentures will be reduced to the original interest rate.
Additional Interest shall be computed based on the actual number of days
elapsed in each 90-day period in which the Shelf Registration Statement is
unusable.

         The Company shall notify the Trustee within three business days after
each and every date on which an event occurs in respect of which Additional
Interest is required to be paid (an "Event Date"). Additional Interest shall be
paid by the Company by depositing with the Trustee, in trust, for the benefit
of the Holders of Debentures, on or before the applicable semiannual interest
payment date, immediately available funds in an amount sufficient to pay the
Additional Interest then due. The Additional Interest due shall be payable on
each interest payment date to

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the Holder of Debentures entitled to receive the interest payment to be paid on
such date as set forth in the Indenture. Each obligation to pay Additional
Interest shall be deemed to accrue from and including the day following the
applicable Event Date.

         3.       Registration Procedures.

         In connection with the obligations of the Company with respect to the
Shelf Registration Statement, the Company shall:

                  (a) prepare and file with the SEC a Shelf Registration
Statement, within the relevant time period specified in Section 2, on the
appropriate form under the 1933 Act, which form (i) shall be selected by the
Company, (ii) shall be available for the sale of the Debentures by the selling
beneficial owners thereof, (iii) shall comply as to form in all material
respects with the requirements of the applicable form and include or
incorporate by reference all financial statements required by the SEC to be
filed therewith or incorporated by reference therein, and (iv) shall comply in
all respects with the requirements of Regulation S-T under the 1933 Act;

                  (b) prepare and file with the SEC such amendments and
post-effective amendments to the Shelf Registration Statement as may be
necessary under applicable law to keep the Shelf Registration Statement
effective for the Effectiveness Period; and cause each Prospectus to be
supplemented by any required prospectus supplement, and as so supplemented to
be filed pursuant to Rule 424 (or any similar provision then in force) under
the 1933 Act and comply with the provisions of the 1933 Act, the 1934 Act and
the rules and regulations thereunder applicable to them with respect to the
disposition of all Debentures covered by the Shelf Registration Statement
during the Effectiveness Period in accordance with the plan of distribution
included in the Prospectus;

                  (c) (i) notify each beneficial owner (or, in the case of
Debentures held through the Depositary, the participant in the Depositary
through whom such beneficial owner holds) of Debentures, at least five business
days prior to filing, that a Shelf Registration Statement with respect to the
Debentures is being filed and advising such beneficial owners that the
distribution of Debentures will be made in accordance with the method selected
by the Majority Holders participating in the Shelf Registration; (ii) furnish
to each beneficial owner of Debentures and to each underwriter of an
underwritten offering of Debentures, if any, without charge, as many copies of
each Prospectus, including each preliminary Prospectus, and any amendment or
supplement thereto and such other documents as such beneficial owner or
underwriter may reasonably request, including financial statements and
schedules and, if the beneficial owner so requests, all exhibits in order to
facilitate the public sale or other disposition of the Debentures; and (iii)
hereby consent to the use of the Prospectus or any amendment or supplement
thereto by each of the selling beneficial owner of Debentures in connection
with the offering and sale of the Debentures covered by the Prospectus or any
amendment or supplement thereto;

                  (d) use its reasonable best efforts to register or qualify
the Debentures under all applicable state securities or "blue sky" laws of such
jurisdictions as any beneficial owner of Debentures covered by any Shelf
Registration Statement and each underwriter of an underwritten

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offering of Debentures shall reasonably request by the time the Shelf
Registration Statement is declared effective by the SEC, and do any and all
other acts and things which may be reasonably necessary or advisable to enable
each such beneficial owner and underwriter to consummate the disposition in
each such jurisdiction of such Debentures owned by such beneficial owner;
provided, however, that the Company shall not be required to (i) qualify as a
foreign corporation or as a dealer in securities in any jurisdiction where it
would not otherwise be required to qualify but for this Section 3(d), (ii) take
any action which would subject it to general service of process or taxation in
any such jurisdiction where it is not then so subject, or (iii) conform its
capitalization or the composition of its assets at the time to the securities
or blue sky laws of such jurisdiction;

                  (e) notify promptly each beneficial owner of Debentures (i)
when the Shelf Registration Statement has become effective and when any
post-effective amendments and supplements thereto become effective, (ii) of any
request by the SEC or any state securities authority for post-effective
amendments and supplements to the Shelf Registration Statement and Prospectus
or for additional information after the Registration Statement has become
effective, (iii) of the issuance by the SEC or any state securities authority
of any stop order suspending the effectiveness of the Shelf Registration
Statement or the initiation of any proceedings for that purpose, (iv) if,
between the effective date of the Shelf Registration Statement and the closing
of any sale of Debentures covered thereby, the representations and warranties
of the Company contained in any underwriting agreement, securities sales
agreement or other similar agreement, if any, relating to the offering cease to
be true and correct in all material respects, (v) of the happening of any event
or the discovery of any facts during the period the Shelf Registration
Statement is effective which makes any statement made in the Shelf Registration
Statement or the related Prospectus untrue in any material respect or which
requires the making of any changes in the Shelf Registration Statement or
Prospectus in order to make the statements therein not misleading, (vi) of the
receipt by the Company of any notification with respect to the suspension of
the qualification of the Debentures for sale in any jurisdiction or the
initiation or threatening of any proceeding for such purpose and (vii) of any
determination by the Company that a post-effective amendment to the Shelf
Registration Statement would be appropriate;

                  (f) furnish Brown & Wood LLP, as special counsel for the
Holders of Debentures (or, if Brown & Wood LLP is unable or unwilling to
serve), such other special counsel (but not more than one) as may be selected
by the Majority Holders ("Special Counsel"), copies of any comment letters
received from the SEC or any other request by the SEC or any state securities
authority for amendments or supplements to a Shelf Registration Statement and
Prospectus or for additional information;

                  (g) make every reasonable effort to obtain the withdrawal of
any order suspending the effectiveness of the Shelf Registration Statement at
the earliest possible moment;

                  (h) furnish to each beneficial owner of Debentures, and each
underwriter, if any, without charge, at least one conformed copy of the Shelf
Registration Statement and any

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post-effective amendment thereto, including financial statements and schedules
(without documents incorporated therein by reference and all exhibits thereto,
unless requested);

                  (i) facilitate the timely preparation and delivery of a new
global certificate representing Debentures which have been sold through the
Registration Statement that does not bear any restrictive legends;

                  (j) upon the occurrence of any event or the discovery of any
facts, such as contemplated by Sections 3(e)(v) and 3(e)(vii) hereof, as
promptly as practicable after the occurrence of such an event, use its
reasonable best efforts to prepare a supplement or post-effective amendment to
the Shelf Registration Statement or the related Prospectus or any document
incorporated therein by reference or file any other required document so that,
as thereafter delivered to the purchasers of the Debentures, such Prospectus
will not contain at the time of such delivery any untrue statement of a
material fact or omit to state a material fact necessary to make the statements
therein, in light of the circumstances under which they were made, not
misleading. At such time as such public disclosure is otherwise made or the
Company determines that such disclosure is not necessary, in each case to
correct any misstatement of a material fact or to include any omitted material
fact, the Company agrees promptly to notify each beneficial owner of such
determination and to furnish each beneficial owner such number of copies of the
Prospectus as amended or supplemented, as such Holder may reasonably request;

                  (k) obtain a CUSIP number for the new global certificate
referred to in Section 3(i), above, not later than the effective date of the
Shelf Registration Statement;

                  (l) (i) cause the Indenture to be qualified under the Trust
Indenture Act of 1939, as amended, in connection with the registration of the
Debentures, (ii) cooperate with the Trustee and the Holders to effect such
changes to the Indenture as may be required for the Indenture to be so
qualified in accordance with the terms of the TIA and (iii) execute, and use
its reasonable best efforts to cause the Trustee to execute, all documents as
may be required to effect such changes, and all other forms and documents
required to be filed with the SEC to enable the Indenture to be so qualified in
a timely manner;

                  (m) enter into agreements (including underwriting agreements
containing usual and customary terms) and take all other customary and
appropriate actions in order to expedite or facilitate the disposition of such
Debentures and in such connection whether or not an underwriting agreement is
entered into and whether or not the registration is an underwritten
registration:

                  (i) make such representations and warranties to the
         beneficial owners of Debentures named as selling security holders in
         the Prospectus and the underwriters, if any, in form, substance and
         scope as are customarily made by issuers to underwriters in similar
         underwritten offerings as may be reasonably requested by them;

                  (ii) obtain opinions of counsel to the Company (which counsel
         and opinions (in form, scope and substance) shall be reasonably
         satisfactory to the managing

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         underwriters, if any, and the beneficial owners of a majority in
         principal amount of the Debentures being sold) addressed to beneficial
         owners of Debentures named as selling security holders in the
         Prospectus and the underwriters, if any, covering the matters
         customarily covered in opinions requested in sales of securities or
         underwritten offerings and such other matters as may be reasonably
         requested by such Holders and underwriters;

                  (iii) obtain "cold comfort" letters and updates thereof from
         the Company's independent certified public accountants (and, if
         necessary, any other independent certified public accountants of any
         subsidiary of the Company or of any business acquired by the Company
         for which financial statements are, or are required to be, included in
         the Shelf Registration Statement) addressed to the underwriters, if
         any, and use reasonable efforts to have such letter addressed to the
         beneficial owners of Debentures named as selling security holders in
         the Prospectus (to the extent consistent with SAS 72), such letters to
         be in customary form and covering matters of the type customarily
         covered in "cold comfort" letters to underwriters in connection with
         similar underwritten offerings;

                  (iv) enter into a securities sales agreement with the
         beneficial owners and an agent of the beneficial owners providing for,
         among other things, the appointment of such agent for the selling
         beneficial owners for the purpose of soliciting purchases of
         Debentures, which agreement shall be in form, substance and scope
         customary for similar offerings;

                  (v) if an underwriting agreement is entered into, cause the
         same to set forth indemnification provisions and procedures
         substantially equivalent to the indemnification provisions and
         procedures set forth in Section 4 hereof with respect to the
         underwriters and all other parties to be indemnified pursuant to said
         Section or, at the request of any underwriters, in the form
         customarily provided to such underwriters in similar types of
         transactions; and

                  (vi) deliver such documents and certificates as may be
         reasonably requested and as are customarily delivered in similar
         offerings to the beneficial owners of a majority in principal amount
         of the Debentures being sold and the managing underwriters, if any.

The above shall be done at (i) the effectiveness of the Shelf Registration
Statement (and each post-effective amendment thereto) and (ii) each closing
under any underwriting or similar agreement as and to the extent required
thereunder;

                  (n) make available for inspection by representatives of the
beneficial owners of the Debentures, any underwriters participating in any
disposition pursuant to the Shelf Registration Statement, any Special Counsel
or any accountant retained by any of the foregoing, all financial and other
records, pertinent corporate documents and properties of the Company reasonably
requested by any such persons, and cause the respective officers, directors,
employees, and any other agents of the Company to supply all information
reasonably requested

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by any such representative, underwriter, Special Counsel or accountant in
connection with the Shelf Registration Statement, and make such representatives
of the Company available for discussion of such documents as shall be
reasonably requested by the Initial Purchaser; provided, however, that the
Company shall be entitled to first obtain a customary confidentiality agreement
from any such Person;

                  (o) at least five business days prior to filing the Shelf
Registration Statement or any amendment to the Shelf Registration Statement,
provide copies of such document to each beneficial owner (or, in the case of
Debentures held through the Depositary, the participant in the Depositary
through whom such beneficial owner holds) of Debentures, to the Initial
Purchaser, to Special Counsel and to the underwriter or underwriters of an
underwritten offering of Debentures, if any, make such changes in any such
document prior to the filing thereof as the Initial Purchaser, Special Counsel
or the underwriter or underwriters reasonably request and not file any such
document in a form to which the Majority Holders of Debentures, the Initial
Purchaser on behalf of the beneficial owners of Debentures, Special Counsel or
any underwriter shall not have previously been advised and furnished a copy of
or to which such Majority Holders, the Initial Purchaser of behalf of the
beneficial owners of Debentures, Special Counsel or any underwriter shall
reasonably object, and make the representatives of the Company available for
discussion of such document as shall be reasonably requested by the beneficial
owners of Debentures, the Initial Purchaser on behalf of such beneficial
owners, Special Counsel or any underwriter.

                  (p) otherwise comply with all applicable rules and
regulations of the SEC and make available to its security holders, as soon as
reasonably practicable, an earnings statement covering at least 12 months which
shall satisfy the provisions of Section 11(a) of the 1933 Act and Rule 158
thereunder; and

                  (q) cooperate and assist in any filings required to be made
with the NASD and in the performance of any due diligence investigation by any
underwriter and its counsel (including any "qualified independent underwriter"
that is required to be retained in accordance with the rules and regulations of
the NASD); and

         The Company may (as a condition to any beneficial owner's
participation in the Shelf Registration) require each beneficial owner of
Debentures to furnish to the Company such information regarding the beneficial
owner and the proposed distribution by such beneficial owner of its Debentures
as the Company may from time to time reasonably request in writing for use in
connection with the Shelf Registration Statement or Prospectus included
therein, including without limitation, information specified in Item 507 of
Regulation S-K under the 1933 Act.

         Each beneficial owner agrees that, upon receipt of any notice from the
Company of the happening of any event or the discovery of any facts, each of
the kind described in Section 3(e)(v) hereof, such beneficial owner will
forthwith discontinue disposition of Debentures pursuant to the Shelf
Registration Statement until such beneficial owner's receipt of the copies of
the supplemented or amended Prospectus contemplated by Section 3(j) hereof,
and, if so directed by the Company, such beneficial owner will deliver to the
Company (at its expense) all copies in

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such beneficial owner's possession, other than permanent file copies then in
such Holder's possession, of the Prospectus covering such Debentures current at
the time of receipt of such notice.

         If any of the Debentures covered by any Shelf Registration Statement
are to be sold in an underwritten offering, the underwriter or underwriters and
manager or managers that will manage such offering will be selected by the
Majority Holders of such Debentures included in such offering, provided such
selection is acceptable to the Company. No beneficial owner of Debentures may
participate in any underwritten registration hereunder unless such beneficial
owner (a) agrees to sell such beneficial owner's Debentures on the basis
provided in any underwriting arrangements approved by the persons entitled
hereunder to approve such arrangements and (b) completes and executes all
questionnaires, powers of attorney, indemnities, underwriting agreements and
other documents required under the terms of such underwriting arrangements.

         4.       Indemnification; Contribution.

                  (a) The Company agrees to indemnify and hold harmless the
Initial Purchaser, each beneficial owner named as a selling security holder in
the Prospectus, each Person who participates as an underwriter (any such Person
being an "Underwriter") and each Person, if any, who controls any beneficial
owner named as a selling security holder in the Prospectus or Underwriter
within the meaning of Section 15 of the 1933 Act or Section 20 of the 1934 Act
as follows:

                  (i) against any and all loss, liability, claim, damage and
         expense, as incurred, arising out of any untrue statement or alleged
         untrue statement of a material fact contained in the Shelf
         Registration Statement (or any amendment or supplement thereto)
         pursuant to which Debentures were registered under the 1933 Act,
         including all documents incorporated therein by reference, or the
         omission or alleged omission therefrom of a material fact required to
         be stated therein or necessary to make the statements therein not
         misleading, or arising out of any untrue statement or alleged untrue
         statement of a material fact contained in any Prospectus (or any
         amendment or supplement thereto) or the omission or alleged omission
         therefrom of a material fact necessary in order to make the statements
         therein, in the light of the circumstances under which they were made,
         not misleading;

                  (ii) against any and all loss, liability, claim, damage and
         expense, as incurred, to the extent of the aggregate amount paid in
         settlement of any litigation, or any investigation or proceeding by
         any governmental agency or body, commenced or threatened, or of any
         claim based upon any such untrue statement or omission, or any such
         alleged untrue statement or omission; provided that (subject to
         Section 4(d) below) any such settlement is effected with the written
         consent of the Company; and

                  (iii) against any and all expense, as incurred (including the
         fees and disbursements of counsel chosen by any indemnified party as
         provided therein),

                                      11
<PAGE>   13

         reasonably incurred in investigating or defending against any
         litigation, or any investigation or proceeding by any governmental
         agency or body, commenced or threatened, or any claim based upon any
         such untrue statement or omission, or any such alleged untrue
         statement or omission, to the extent that any such expense is not paid
         under subparagraph (i) or (ii) above;

provided, however, that this indemnity agreement shall not apply to any loss,
liability, claim, damage or expense to the extent arising out of any untrue
statement or omission or alleged untrue statement or omission made in reliance
upon and in conformity with written information furnished to the Company by the
beneficial owner or Underwriter expressly for use in the Shelf Registration
Statement (or any amendment thereto) or any Prospectus (or any amendment or
supplement thereto), and provided further, that the Company shall not indemnify
any Underwriter or any person who controls such Underwriter from any loss,
liability, claim or damage (or expense incurred in connection therewith)
alleged by any person who purchased Debentures from such Underwriter if the
untrue statement, omission or allegation thereof upon which such loss,
liability, claim or damage is based was made in (i) any preliminary prospectus,
if a copy of the Prospectus (as then amended or supplemented if the Company
shall have furnished any amendments or supplements thereto) was not sent or
given by or on behalf of such Underwriter to such person at or prior to the
written confirmation of the sale of Debentures to such person, and if the
Prospectus (as so amended or supplemented) corrected the untrue statement or
omission giving rise to such loss, claim, damage or liability; (ii) any
Prospectus used by such Underwriter or any Person who controls such
Underwriter, after such time as the Company advised the Underwriters that the
filing of a post-effective amendment or supplement thereto was required, except
the Prospectus as so amended or supplemented, if the Prospectus as amended or
supplemented by such post-effective amendment or supplement would not have
given rise to such loss, liability, claim or damage; or (iii) any Prospectus
used after such time as the obligation of the Company to keep the same current
and effective has expired.

         (b)      Each beneficial owner severally, but not jointly, agrees to
indemnify and hold harmless the Company, the Initial Purchaser, each
Underwriter and the other selling beneficial owners, and each of their
respective directors and officers, and each Person, if any, who controls the
Company, the Initial Purchaser, any Underwriter or any other selling beneficial
owner within the meaning of Section 15 of the 1933 Act or Section 20 of the
1934 Act, against any and all loss, liability, claim, damage and expense
described in the indemnity contained in Section 4(a) hereof, as incurred, but
only with respect to untrue statements or omissions, or alleged untrue
statements or omissions, made in the Shelf Registration Statement (or any
amendment thereto) or any Prospectus included therein (or any amendment or
supplement thereto) in reliance upon and in conformity with written information
with respect to such beneficial owner furnished to the Company by such
beneficial owner expressly for use in the Shelf Registration Statement (or any
amendment thereto) or such Prospectus (or any amendment or supplement thereto);
provided, however, that no such beneficial owner shall be liable for any claims
hereunder in excess of the amount of net proceeds received by such beneficial
owner from the sale of Debentures pursuant to the Shelf Registration Statement.

                                      12
<PAGE>   14

         (c)      Each indemnified party shall give written notice as promptly
as reasonably practicable to each indemnifying party of any action or
proceeding commenced against it in respect of which indemnity may be sought
hereunder, and the indemnifying party shall assume the defense thereof,
including the employment of counsel satisfactory to the indemnified party, and
the payment of all expenses. Any omission to so notify an indemnifying party
shall not relieve such indemnifying party from any liability hereunder to the
extent it is not materially prejudiced as a result thereof and in any event
shall not relieve it from any liability which it may have otherwise than on
account of this indemnity agreement. Any such indemnified party shall have the
right to employ separate counsel in any such action or proceeding and to
participate in the defense thereof, but the fees and expenses of such separate
counsel shall be paid by such indemnified party unless (a) the indemnifying
party has agreed to pay such fees and expenses or (b) the indemnifying party
shall have failed to assume the defense of such action or proceeding and employ
counsel reasonably satisfactory to the indemnified party in any such action or
proceeding or (c) the named parties to any such action or proceeding (including
any impleaded parties) include both such indemnified party and indemnifying
party, and the indemnified party shall have been advised by its counsel that
there may be a conflict of interest between such indemnified party and
indemnifying party in the conduct of the defense of such action (in which case,
if such indemnified party notifies the indemnifying party in writing that it
elects to employ separate counsel at the expense of the indemnifying party, the
indemnifying party shall not have the right to assume the defense of such
action or proceeding on behalf of such indemnified party), it being understood,
however, that the indemnifying party shall not, in connection with any one such
action or proceeding or separate but substantially similar or related actions
or proceedings arising out of the same general allegations or circumstances, be
liable for the reasonable fees and expenses of more than one separate firm of
attorneys (unless the members of such firm are not admitted to practice in a
jurisdiction where an action is pending, in which case the indemnifying party
shall pay the reasonable fees and expenses of one additional firm of attorneys
to act as local counsel in such jurisdiction, provided the services of such
counsel are substantially limited to that of appearing as attorneys of record)
at any time for all indemnified parties, which firm shall be designated in
writing by the indemnified party. No indemnifying party shall, without the
prior written consent of the indemnified parties, settle or compromise or
consent to the entry of any judgment with respect to any litigation, or any
investigation or proceeding by any governmental agency or body, commenced or
threatened, or any claim whatsoever in respect of which indemnification or
contribution could be sought under this Section 4 (whether or not the
indemnified parties are actual or potential parties thereto), unless such
settlement, compromise or consent (i) includes an unconditional release of each
indemnified party from all liability arising out of such litigation,
investigation, proceeding or claim and (ii) does not include a statement as to
or an admission of fault, culpability or a failure to act by or on behalf of
any indemnified party.

         (d)      If at any time an indemnified party shall have requested an
indemnifying party to reimburse the indemnified party for fees and expenses of
counsel, such indemnifying party agrees that it shall be liable for any
settlement of the nature contemplated by Section 4(a)(ii) effected without its
written consent if (i) such settlement is entered into more than 45 days after
receipt by such indemnifying party of the aforesaid request, (ii) such
indemnifying

                                      13
<PAGE>   15

party shall have received notice of the terms of such settlement at least 30
days prior to such settlement being entered into and (iii) such indemnifying
party shall not have reimbursed such indemnified party in accordance with such
request prior to the date of such settlement.

         (e)      If the indemnification provided for in this Section 4 is for
any reason unavailable to hold harmless an indemnified party (other than by
reason of the first sentence of Section 4(c)) in respect of any losses,
liabilities, claims, damages or expenses referred to therein, then each
indemnifying party shall contribute to the aggregate amount of such losses,
liabilities, claims, damages and expenses incurred by such indemnified party,
as incurred, (i) in such proportion as is appropriate to reflect the relative
benefits received by the Company on the one hand and the beneficial owners and
the Initial Purchaser on the other hand from the offering of the Debentures
included in such offering or (ii) if the allocation provided by clause (i) is
not permitted by applicable law, in such proportion as is appropriate to
reflect not only the relative benefits referred to in clause (i) above but also
the relative fault of the Company on the one hand and the beneficial owners and
the Initial Purchaser on the other hand in connection with the statements or
omissions which resulted in such losses, liabilities, claims, damages or
expenses, as well as any other relevant equitable considerations.

         The relative benefits received by the Company on the one hand and the
beneficial owners and the Initial Purchaser on the other hand in connection
with the offering of the Debentures included in such offering shall be deemed
to be in the same respective proportions as the total net proceeds from the
offering of the Debentures pursuant to the Purchase Agreement (before deducting
expenses) received by the Company and the total underwriting discount received
by the Initial Purchaser, bear to the aggregate initial offering price of the
Debentures.

         The relative fault of the Company on the one hand and the beneficial
owners and the Initial Purchaser on the other hand shall be determined by
reference to, among other things, whether any such untrue or alleged untrue
statement of a material fact or omission or alleged omission to state a
material fact relates to information supplied by the Company, the beneficial
owners or the Initial Purchaser and the parties' relative intent, knowledge,
access to information and opportunity to correct or prevent such statement or
omission.

         The Company, the beneficial owners and the Initial Purchaser agree
that it would not be just and equitable if contribution pursuant to this
Section 4 were determined by pro rata allocation (even if the Holders and the
Initial Purchaser were treated as one entity for such purpose) or by any other
method of allocation which does not take account of the equitable
considerations referred to above in this Section 4. The aggregate amount of
losses, liabilities, claims, damages and expenses incurred by an indemnified
party and referred to above in this Section 4 shall be deemed to include any
legal or other expenses reasonably incurred by such indemnified party in
investigating, preparing or defending against any litigation, or any
investigation or proceeding by any governmental agency or body, commenced or
threatened, or any claim whatsoever based upon any such untrue or alleged
untrue statement or omission or alleged omission.

                                      14
<PAGE>   16

         Notwithstanding the provisions of this Section 4, the Initial
Purchaser shall not be required to contribute any amount in excess of the
amount by which the total price at which the Debentures purchased and sold by
it were offered exceeds the amount of any damages which the Initial Purchaser
has otherwise been required to pay by reason of such untrue or alleged untrue
statement or omission or alleged omission.

         No Person guilty of fraudulent misrepresentation (within the meaning
of Section 11(f) of the 1933 Act) shall be entitled to contribution from any
Person who was not guilty of such fraudulent misrepresentation.

         For purposes of this Section 4, each Person, if any, who controls an
Initial Purchaser or beneficial owner within the meaning of Section 15 of the
1933 Act or Section 20 of the 1934 Act shall have the same rights to
contribution as such Initial Purchaser or beneficial owner, and each Person, if
any, who controls the Company within the meaning of Section 15 of the 1933 Act
or Section 20 of the 1934 Act shall have the same rights to contribution as the
Company.

         5.       Miscellaneous.

         5.1      Rule 144 and Rule 144A. For so long as the Company is subject
to the reporting requirements of Section 13 or 15 of the 1934 Act, the Company
covenants that it will file the reports required to be filed by it under the
1933 Act and Section 13(a) or 15(d) of the 1934 Act and the rules and
regulations adopted by the SEC thereunder. If the Company ceases to be so
required to file such reports, the Company covenants that it will upon the
request of any beneficial owner of Debentures (a) deliver to a prospective
purchaser such information as is necessary to permit sales pursuant to Rule
144A under the 1933 Act and it will take such further action as any beneficial
owner of Debentures may reasonably request, and (b) take such further action
that is reasonable in the circumstances, in each case, to the extent required
from time to time to enable such beneficial owner to sell its Debentures
without registration under the 1933 Act within the limitation of the exemptions
provided by (i) Rule 144 under the 1933 Act, as such Rule may be amended from
time to time, (ii) Rule 144A under the 1933 Act, as such Rule may be amended
from time to time, or (iii) any similar rules or regulations hereafter adopted
by the SEC. Upon the request of any beneficial owner of Debentures, the Company
will deliver to such beneficial owner a written statement as to whether it has
complied with such requirements. The Company's obligations under this Section
5.1 shall terminate upon the consummation of the Effectiveness Period.

         5.2      No Inconsistent Agreements. The Company has not entered into
and the Company will not after the date of this Agreement enter into any
agreement which is inconsistent with the rights granted to the beneficial
owners of Debentures in this Agreement or otherwise conflicts with the
provisions hereof. The rights granted to the beneficial owners hereunder do not
and will not for the term of this Agreement in any way conflict with the rights
granted to the holders of the Company's other issued and outstanding securities
under any such agreements.

         5.3      Amendments and Waivers. The provisions of this Agreement,
including the provisions of this sentence, may not be amended, modified or
supplemented, and waivers or

                                      15
<PAGE>   17

consents to departures from the provisions hereof may not be given unless the
Company has obtained the written consent of beneficial owners of at least a
majority in aggregate principal amount of the outstanding Debentures affected
by such amendment, modification, supplement, waiver or departure.

         5.4      Notices. All notices and other communications provided for or
permitted hereunder shall be made in writing by hand delivery, registered
first-class mail, telecopier, or any courier guaranteeing overnight delivery
(a) if to a beneficial owner, at the most current address given by such
beneficial owner to the Company by means of a notice given in accordance with
the provisions of this Section 5.4, which address initially is the address set
forth in the Purchase Agreement with respect to the Initial Purchaser; and (b)
if to the Company, initially at the Company's address set forth in the Purchase
Agreement, and thereafter at such other address of which notice is given in
accordance with the provisions of this Section 5.4.

         All such notices and communications shall be deemed to have been duly
given: at the time delivered by hand, if personally delivered; two business
days after being deposited in the mail, postage prepaid, if mailed; when
receipt is acknowledged, if telecopied; and on the next business day if timely
delivered to an air courier guaranteeing overnight delivery.

         Copies of all such notices, demands, or other communications shall be
concurrently delivered by the person giving the same to the Trustee under the
Indenture, at the address specified in such Indenture.

         5.5      Successor and Assigns. This Agreement shall inure to the
benefit of and be binding upon the successors, assigns and transferees of each
of the parties, including, without limitation and without the need for an
express assignment, beneficial owners of the Debentures; provided that nothing
herein shall be deemed to permit any assignment, transfer or other disposition
of Debentures in violation of the terms of the Purchase Agreement or the
Indenture. If any transferee of the Initial Purchaser or any other beneficial
owner shall acquire Debentures, in any manner, whether by operation of law or
otherwise, such Debentures shall be held subject to all of the terms of this
Agreement, and by taking and holding such Debentures such Person shall be
conclusively deemed to have agreed to be bound by and to perform all of the
terms and provisions of this Agreement, including the restrictions on resale
set forth in this Agreement and, if applicable, the Purchase Agreement, and
such Person shall be entitled to receive the benefits hereof.

         5.6      Third Party Beneficiaries. The beneficial owners of the
Debentures shall be third party beneficiaries to the agreements made hereunder
between the Company, on the one hand, and the Initial Purchaser, on the other
hand, and shall have the right to enforce such agreements directly to the
extent they deem such enforcement necessary or advisable to protect their
rights.

         5.7      Specific Enforcement. Without limiting the remedies available
to the Initial Purchaser and the beneficial owners, the Company acknowledges
that any failure by the Company to comply with its obligations under Sections
2.1 through 2.3 hereof may result in material irreparable injury to the Initial
Purchaser or the beneficial owners for which there is no

                                      16
<PAGE>   18

adequate remedy at law, that it would not be possible to measure damages for
such injuries precisely and that, in the event of any such failure, the Initial
Purchaser or any beneficial owner may obtain such relief as may be required to
specifically enforce the Company's obligations under Sections 2.1 through 2.3
hereof.

         5.8      Counterparts. This Agreement may be executed in any number of
counterparts and by the parties hereto in separate counterparts, each of which
when so executed shall be deemed to be an original and all of which taken
together shall constitute one and the same agreement.

         5.9      Headings. The headings in this Agreement are for convenience
of reference only and shall not limit or otherwise affect the meaning hereof.

         5.10     GOVERNING LAW. THIS AGREEMENT SHALL BE GOVERNED BY AND
CONSTRUED IN ACCORDANCE WITH THE LAW OF THE STATE OF NEW YORK WITHOUT REGARD TO
THE PRINCIPLES OF CONFLICT OF LAWS THEREOF.

         5.11     Severability. In the event that any one or more of the
provisions contained herein, or the application thereof in any circumstance, is
held invalid, illegal or unenforceable, the validity, legality and
enforceability of any such provision in every other respect and of the
remaining provisions contained herein shall not be affected or impaired
thereby.

                                      17
<PAGE>   19

         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first written above.

                                   LIBERTY MEDIA CORPORATION

                                   By:
                                        ---------------------------------------
                                         Name:   David Flowers
                                         Title:  Vice President and Treasurer

Confirmed and accepted as
   of the date first above
   written:

SALOMON SMITH BARNEY INC.

By:
    -----------------------------
     Name:
     Title:  Authorized Signatory<PAGE>   1
                                                                    EXHIBIT 4.13

                            FORM OF 3-3/4% DEBENTURE

THE HOLDER OF THIS SECURITY BY ITS ACCEPTANCE HEREOF IS DEEMED TO HAVE AGREED TO
BE BOUND BY THE PROVISIONS OF A REGISTRATION RIGHTS AGREEMENT BETWEEN LIBERTY
AND THE INITIAL PURCHASER NAMED THEREIN, DATED FEBRUARY 10, 2000 (THE
"REGISTRATION RIGHTS AGREEMENT"). LIBERTY WILL PROVIDE A COPY OF THE
REGISTRATION RIGHTS AGREEMENT TO SUCH HOLDER WITHOUT CHARGE UPON WRITTEN REQUEST
TO LIBERTY AT ITS PRINCIPAL PLACE OF BUSINESS.

THE SECURITY EVIDENCED HEREBY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT
OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR ANY STATE OR OTHER SECURITIES
LAWS. NEITHER THIS SECURITY NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE
REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE
DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS THE TRANSACTION IS
EXEMPT FROM, OR NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES
ACT. THE HOLDER OF THIS SECURITY BY ITS ACCEPTANCE HEREOF (1) REPRESENTS THAT
(A) IT IS A "QUALIFIED INSTITUTIONAL BUYER" (AS DEFINED IN RULE 144A UNDER THE
SECURITIES ACT), (B) IT IS AN INSTITUTIONAL "ACCREDITED INVESTOR" WITHIN THE
MEANING OF SUBPARAGRAPH (a)(1), (2), (3) OR (7) OF RULE 501 UNDER THE SECURITIES
ACT OR (C) IT IS NOT A U.S. PERSON AND IS ACQUIRING THIS SECURITY IN AN
"OFFSHORE TRANSACTION" PURSUANT TO RULE 903 OR 904 OF REGULATION S, (2) AGREES
THAT IT WILL NOT PRIOR TO (X) THE DATE WHICH IS TWO YEARS (OR SUCH SHORTER
PERIOD OF TIME AS PERMITTED BY RULE 144(k) UNDER THE SECURITIES ACT OR ANY
SUCCESSOR PROVISION THEREUNDER) AFTER THE LATER OF THE ORIGINAL ISSUE DATE
HEREOF (OR OF ANY PREDECESSOR OF THIS SECURITY) OR THE LAST DAY ON WHICH LIBERTY
OR ANY AFFILIATE OF LIBERTY WAS THE OWNER OF THIS SECURITY (OR ANY PREDECESSOR
OF THIS SECURITY) AND (Y) SUCH LATER DATE, IF ANY, AS MAY BE REQUIRED BY
APPLICABLE LAWS (THE "RESALE RESTRICTION TERMINATION DATE"), OFFER, SELL OR
OTHERWISE TRANSFER THIS SECURITY EXCEPT (A) TO LIBERTY OR ANY SUBSIDIARY
THEREOF, (B) PURSUANT TO A REGISTRATION STATEMENT WHICH HAS BEEN DECLARED
EFFECTIVE UNDER THE SECURITIES ACT, (C) FOR SO LONG AS THE SECURITIES ARE
ELIGIBLE FOR RESALE PURSUANT TO RULE 144A, TO A PERSON IT REASONABLY BELIEVES IS
A "QUALIFIED INSTITUTIONAL BUYER" AS DEFINED IN RULE 144A UNDER THE SECURITIES
ACT THAT PURCHASES FOR ITS OWN ACCOUNT OR FOR THE ACCOUNT OF A QUALIFIED
INSTITUTIONAL BUYER TO WHOM NOTICE IS GIVEN THAT THE TRANSFER IS BEING MADE IN
RELIANCE ON RULE 144A, (D) INSIDE THE UNITED STATES TO AN INSTITUTIONAL
"ACCREDITED INVESTOR" WITHIN THE MEANING OF SUBPARAGRAPH (a)(1), (2), (3) OR (7)
OF RULE 501 UNDER THE SECURITIES ACT THAT PRIOR TO SUCH TRANSFER, FURNISHES (OR
HAS FURNISHED ON ITS BEHALF BY A U.S. BROKER-DEALER) TO THE TRUSTEE OR TRANSFER
AGENT, A SIGNED LETTER CONTAINING CERTAIN REPRESENTATIONS AND AGREEMENTS
RELATING TO THE RESTRICTIONS ON TRANSFER OF THIS SECURITY (THE FORM OF WHICH
LETTER CAN BE OBTAINED FROM THE TRUSTEE OR TRANSFER AGENT FOR THIS SECURITY),
(E) PURSUANT TO OFFERS AND SALES TO NON-U.S. PERSONS THAT OCCUR OUTSIDE THE
UNITED STATES WITHIN THE MEANING OF REGULATION S UNDER THE SECURITIES ACT,
PURSUANT TO RULE 904 OF REGULATION S OR (F) PURSUANT TO ANOTHER AVAILABLE
EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT, AND (3)
AGREES THAT IT WILL GIVE TO EACH PERSON TO WHOM THIS SECURITY IS TRANSFERRED A
NOTICE SUBSTANTIALLY TO THE EFFECT OF THIS LEGEND; PROVIDED THAT LIBERTY, THE

<PAGE>   2

TRUSTEE AND THE TRANSFER AGENT AND REGISTRAR RESERVE THE RIGHT PRIOR TO ANY
OFFER, SALE OR OTHER TRANSFER PURSUANT TO CLAUSES (D), (E) OR (F) ABOVE TO
REQUIRE DELIVERY OF AN OPINION OF COUNSEL, CERTIFICATIONS AND OTHER INFORMATION
SATISFACTORY TO LIBERTY, THE TRUSTEE AND THE TRANSFER AGENT AND REGISTRAR. THIS
LEGEND WILL BE REMOVED UPON THE REQUEST OF THE HOLDER AFTER THE RESALE
RESTRICTION TERMINATION DATE. AS USED HEREIN, THE TERMS "OFFSHORE TRANSACTION,"
"UNITED STATES" AND "U.S. PERSON" HAVE THE RESPECTIVE MEANINGS GIVEN TO THEM BY
REGULATION S UNDER THE SECURITIES ACT. IN ANY CASE, ANY HOLDER HEREOF THAT HAS
ACQUIRED THIS SECURITY IN AN "OFFSHORE TRANSACTION" PURSUANT TO RULE 903 OR 904
OF REGULATION S WILL NOT, DIRECTLY OR INDIRECTLY, ENGAGE IN ANY HEDGING
TRANSACTION WITH REGARD TO THIS SECURITY OR ANY SECURITY ISSUABLE UPON EXCHANGE
OF THIS SECURITY EXCEPT AS PERMITTED BY THE SECURITIES ACT.

UNLESS THIS SECURITY IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), TO LIBERTY OR ITS
AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE, OR PAYMENT, AND ANY CERTIFICATE
ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS
REQUESTED BY AN AUTHORIZED REPRESENTATIVE OF DTC (AND ANY PAYMENT IS MADE TO
CEDE & CO. OR TO SUCH OTHER ENTITY AS IS REQUESTED BY AN AUTHORIZED
REPRESENTATIVE OF DTC), ANY TRANSFER, PLEDGE, OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL, INASMUCH AS THE REGISTERED OWNER
HEREOF, CEDE & CO., HAS AN INTEREST HEREIN.

No. R-1                                                             $750,000,000
CUSIP No. 530715AK7

                            LIBERTY MEDIA CORPORATION

                 3 3/4% Senior Exchangeable Debentures due 2030

                               Rule 144A Debenture

         Liberty Media Corporation, a Delaware corporation (hereinafter called
the "Company", which term includes any successor corporation under the Indenture
referred to below), for value received, hereby promises to pay to Cede & Co., or
registered assigns, the amount provided in Section 204 of the Fourth
Supplemental Indenture referred to herein (such amount being referred to herein
as the Maturity Repayment Amount) on February 15, 2030, and to pay interest on
the Original Principal Amount of this Debenture from February 10, 2000, or from
the most recent date to which interest has been paid or provided for,
semiannually on February 15 and August 15 in each year (each, an "Interest
Payment Date"), commencing August 15, 2000, at the rate of 3 3/4% per annum,
until the Maturity Repayment Amount is paid or made available for payment.
Interest on this Debenture shall be calculated on the basis of a 360-day year
consisting of twelve 30-day months. The interest so payable and paid or provided
for on any Interest Payment Date will, as provided in such Indenture, be paid to
the Person in whose name this Debenture (or one or more Predecessor Securities)
is registered at the close of business on the Regular Record Date for such
interest, which shall be the February 1 or August 1 (whether or not a Business
Day), as

                                       2
<PAGE>   3

the case may be, immediately preceding such Interest Payment Date. Any such
interest which is payable, but is not paid or provided for, on any Interest
Payment Date shall forthwith cease to be payable to the registered Holder hereof
on the relevant Regular Record Date by virtue of having been such Holder, and
may be paid to the Person in whose name this Debenture (or one or more
Predecessor Securities) is registered at the close of business on a Special
Record Date for the payment of such Defaulted Interest to be fixed by the
Company, notice whereof shall be given to the Holders of Debentures not less
than 10 days prior to such Special Record Date, or may be paid at any time in
any other lawful manner not inconsistent with the requirements of any securities
exchange on which the Debentures may be listed, and upon such notice as may be
required by such exchange, all as more fully provided in such Indenture.

         Payment of the Maturity Repayment Amount and the interest on this
Debenture will be made at the office or agency of the Company maintained for
that purpose in The Borough of Manhattan, The City of New York, in such coin or
currency of the United States of America as at the time of payment is legal
tender for payment of public and private debts; provided, however, that, at the
option of the Company, interest may be paid by check mailed to the address of
the Person entitled thereto as such address shall appear in the Security
Register; provided, further, that payment to DTC or any successor Depository may
be made by wire transfer to the account designated by DTC or such successor
Depository in writing.

         This Security is a permanent Rule 144A Debenture issued on the date
hereof which represents $750,000,000 of the Original Principal Amount of the
Company's 3 3/4% Senior Exchangeable Debentures due 2030, offered and sold to
qualified institutional buyers, as defined in Rule 144A under the Securities
Act. This Debenture is one of a duly authorized issue of securities of the
Company (herein called the "Debentures") issued and to be issued in one or more
series under an Indenture dated as of July 7, 1999 (herein called, together with
the Fourth Supplemental Indenture referred to below and all other indentures
supplemental thereto, the "Indenture") between the Company and The Bank of New
York, as Trustee (herein called the "Trustee", which term includes any successor
trustee under the Indenture), to which Indenture and all indentures supplemental
thereto reference is hereby made for a statement of the respective rights,
limitations of rights, duties and immunities thereunder of the Company, the
Trustee and the Holders of the Debentures, and of the terms upon which the
Debentures are, and are to be, authenticated and delivered. This Debenture is
one of the series designated on the face hereof, initially limited (subject to
exceptions provided in the Indenture) to the aggregate Original Principal Amount
specified in the Fourth Supplemental Indenture between the Company and the
Trustee, dated as of February 10, 2000, establishing the terms of the Debentures
pursuant to the Indenture (the "Fourth Supplemental Indenture").

         The Debentures are redeemable at the option of the Company, in whole or
in part at any time or from time to time on or after February 15, 2004, on the
terms set forth in Section 208(a) of the Fourth Supplemental Indenture. In
addition, the Debentures are redeemable at the option of the Company upon the
occurrence of a Tax Event or a Share Event or following an Excess Borrow Cost
Period, each as defined in the Fourth Supplemental Indenture, on the terms set
forth in Sections 208(b), (c) and (d), respectively, of the Fourth Supplemental
Indenture.

         The Debentures are exchangeable at the option of the Holders thereof,
on the terms set forth in Section 209 of the Fourth Supplemental Indenture.

                                       3
<PAGE>   4

         If an Event of Default (as defined in the Indenture, including the
amendments thereto in the Fourth Supplemental Indenture) with respect to the
Debentures shall occur and be continuing, the principal of the Debentures may be
declared due and payable in the manner and with the effect provided in the
Indenture.

         The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Securities of each series issued
under the Indenture at any time by the Company and the Trustee with the consent
of the Holders of not less than a majority in aggregate principal amount of the
Securities at the time Outstanding of each series affected thereby. The
Indenture also contains provisions permitting the Holders of specified
percentages in aggregate principal amount of the Securities of any series at the
time Outstanding, on behalf of the Holders of all Securities of such series, to
waive compliance by the Company with certain provisions of the Indenture and
certain past defaults under the Indenture and their consequences. Any such
consent or waiver by the Holder of this Debenture shall be conclusive and
binding upon such Holder and upon all future Holders of this Debenture and of
any Debentures issued upon the registration of transfer hereof or in exchange
herefor or in lieu hereof, whether or not notation of such consent or waiver is
made upon this Debenture or such Debentures.

         No reference herein to the Indenture and no provision of this Debenture
or of the Indenture shall alter or impair the obligation of the Company, which
is absolute and unconditional, to pay the Maturity Repayment Amount and interest
on this Debenture, at the times, place and rate, and in the coin or currency,
herein and in the Indenture prescribed.

         As provided in the Indenture and subject to certain limitations set
forth therein and in this Debenture, the transfer of this Debenture may be
registered on the Security Register upon surrender of this Debenture for
registration of transfer at the office or agency of the Company maintained for
the purpose in any place where the Maturity Repayment Amount and interest on
this Debenture are payable, duly endorsed by, or accompanied by a written
instrument of transfer in form satisfactory to the Company and the Security
Registrar duly executed by, the Holder hereof or by his attorney duly authorized
in writing, and thereupon one or more new Debentures of this series and of like
tenor, of authorized denominations and for the same aggregate Original Principal
Amount, will be issued to the designated transferee or transferees.

         The Debentures are issuable only in registered form without coupons in
the denominations specified in the Fourth Supplemental Indenture establishing
the terms of the Debentures, all as more fully provided in the Indenture. As
provided in the Indenture, and subject to certain limitations set forth in the
Indenture and in this Debenture, the Debentures are exchangeable for a like
aggregate Original Principal Amount of Debentures of this series in different
authorized denominations, as requested by the Holders surrendering the same.

         No service charge shall be made for any such registration of transfer
or exchange, but the Company may require payment of a sum sufficient to cover
any tax or other governmental charge payable in connection therewith, other than
in certain cases provided in the Indenture.

         Prior to due presentment of this Debenture for registration of
transfer, the Company, the Trustee and any agent of the Company or the Trustee
may treat the Person in whose name this

                                       4
<PAGE>   5

Debenture is registered as the owner hereof for all purposes, whether or not
this Debenture be overdue, and neither the Company, the Trustee nor any such
agent shall be affected by notice to the contrary.

         This Debenture shall be governed by and construed in accordance with
the laws of the State of New York.

         All terms used in this Debenture which are defined in the Indenture
shall have the meanings assigned to them in the Indenture.

         Unless the certificate of authentication hereon has been executed by or
on behalf of the Trustee under the Indenture by the manual signature of one of
its authorized signatories, this Debenture shall not be entitled to any benefits
under the Indenture or be valid or obligatory for any purpose.

                                       5
<PAGE>   6

                                                                    EXHIBIT 4.13

                            FORM OF 3-3/4% DEBENTURE

         IN WITNESS WHEREOF, the Company has caused this instrument to be duly
executed.

                                                   LIBERTY MEDIA CORPORATION

Attest:                                            By:
        -----------------------                       --------------------------
        Name:                                         Name:
        Title:                                        Title:

                     TRUSTEE'S CERTIFICATE OF AUTHENTICATION

         This is one of the Debentures of the series designated herein referred
to in the within-mentioned Indenture.

Dated: February 10, 2000                           THE BANK OF NEW YORK,
                                                   as Trustee

                                                   By:
                                                      --------------------------
                                                          Authorized Signatory

                                       6
<PAGE>   7

                             CERTIFICATE OF TRANSFER

         To transfer or assign this Debenture, fill in the form below:

I or we transfer and assign this Debenture to

--------------------------------------------------------------------------------
                       (Insert assignee's tax I.D. number)

--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
              (Print or Type assignee's name, address and zip code)

and irrevocably appoint ________________ agent to transfer this Debenture on the
books of the Company. The agent may substitute another to act for him.

Date:                                    Your signature:
     -------------------                                ------------------------

                                       7
<PAGE>   8

                                   SCHEDULE A

                              SCHEDULE OF EXCHANGES

The following exchanges of Debentures represented by this Rule 144A Debenture
have been made:

<TABLE>
<CAPTION>

                                                 Change in Original      Original Principal
Original Principal                               Principal Amount of     Amount of this Rule
Amount of this Rule                              this Rule 144A          144A Debenture
144A Debenture as of      Date exchange          Debenture due to        following such
February 10, 2000         Made                   Exchange                exchange               Notation made by
------------------------- ---------------------- ----------------------- ---------------------- ----------------------
<S>                       <C>                    <C>                     <C>                    <C>
      $750,000,000
------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

------------------------- ---------------------- ----------------------- ---------------------- ----------------------

========================= ====================== ======================= ====================== ======================
</TABLE>

                                       8

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