Sentence 1: But, as it will never do if John, too, can prove an alibi, she writes him an anonymous note "still copying his hand-writing "which takes him to a remote spot where it is exceedingly unlikely that anyone will see him.

Sentence 2: She was copying someone's handwriting when she wrote the note.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: i've only lived here about six years so if if if i have one it must be very very slight but the Yankees can hear it

Sentence 2: If I have one it is barely noticeable because I have only lived here for about 6 years.
Is this second sentence entailed by the first?

Answer: yes

Sentence 1: As discussed further in text box 4.2, if the projected budget surpluses materialize, the federal government will reach a point at which the projected surpluses will exceed the amount of federal debt available to be redeemed.

Sentence 2: There is no surplus in the federal government.
Is this second sentence entailed by the first?

Answer:
no