Kazukiさんの文は自然な言い方ですよ！
別の言い方もご参考まで。
I was in bed sleeping at the same time yesterday.
「寝ていた」は
I was in bed sleeping
とも言えます。
「昨日のこの時間」は
at the same time yesterday
ご参考になれば幸いです！
1) I was already resting by this time yesterday.
'Resting,' is another common way to say asleep, it is used interchangeably with sleeping, napping, etc.
2) I was sleeping long before this time yesterday.
Saying 'long before' is a well-known, shorter way of saying 'at this time,' or 'at the same time.'
3) This time yesterday I was fast asleep.
'Fast asleep' is a very common phrase meaning deep sleep.
1) I was already resting by this time yesterday.
（昨日のこの時間には寝てました。）
「Resting」は眠っていることを言う別の表現です。「sleeping」「napping」なども使えます。
2) I was sleeping long before this time yesterday.
（昨日のこの時間には寝てました。）
「long before」は良く使われる表現です。「at this time」または「at the same time.」よりも手短な言い方です。
3) This time yesterday I was fast asleep.
（昨日のこの時間には熟睡していました。）
「Fast asleep」は深い眠りを意味するとても一般的な言い回しです。
"At this time" notes the time in which the action happened. "Already" means that something has happened and "asleep" is good to use because that is the way that we say that you were sleeping.
I hope that this helps :)
"At this time" とは、その行為が起こったその時を指します。 "Already" とは、何かが起こってしまったことを意味し、 "asleep"は、眠り落ちたという意味なのでぴったりな表現です。
"At this time yesterday, I was already sleeping."
"I was asleep at this/that time yesterday." (This time - at the time you are talking today, or that time - a time that someone has mentioned.)
At this time - this could mean 8 pm, 9 pm, etc.
Already - meaning before the time that was mentioned.
At this time yesterday, I was already sleeping.
（今日のこの時間には、既に寝ていました。）
I was asleep at this/that time yesterday.
This time - 今日話しているその時、またはthat time - 誰かが述べた時。
At this time - これは、午後8時でも9時でも、他の時間でも意味することができます。
Already - 言及された時間の前の意味。
To explain that you were asleep at this time yesterday, you can say:
"I was already sleeping at this time yesterday."
"Yesterday, I was asleep at this time."
「昨日のこの時間は寝ていた」は次のように言えます。
"I was already sleeping at this time yesterday."（昨日のこの時間はもう寝ていました）
"Yesterday, I was asleep at this time."（昨日のこの時間は寝ていました）
If you are talking about something happening at the same time then you would say 'at this time' or 'by this time'
already means something that has happened before
同じ時間に起きていたことについて言うなら、'at this time'（この時間は）あるいは 'by this time'（この時間までに）と言えます。
'already' は、もう既に起きたことを表します。
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