D.A.F.'s Moadim section

If "the Heavens are for Hashem, and He gave the earth to man," does Hashem supervise what mortal man does on the world below? How did Hashem demonstrate His involvement in the world, through Yetzias Mitzrayim?

1. Mafteach to Shemos 7:14:8:4, especially steps a. thru c.

הלל	Hallel
מוזגים כוס רביעי, וגומרים עליו את ההלל.	Pour the fourth cup, and we complete the Hallel upon it.
לֹא לָנוּ, ה', לֹא לָנוּ, כִּי לְשִׁמְךָ תֵּן כָּבוֹד, עַל חַסְדְּךָ עַל אֲמִתֶּךָ. לָמָּה יֹאמְרוּ הַגּוֹיִם אַיֵּה נָא אֱ-לֹקֵיהֶם. וְאֱ-לֹקֵינוּ בַּשָּׁמַיִם, כֹּל אֲשֶׁר חָפֵץ עָשָׂה. עֲצַבֵּיהֶם כֶּסֶף וְזָהָב מַעֲשֵׂה יְדֵי אָדָם. פֶּה לָהֶם וְלֹא יְדַבֵּרוּ, עֵינַיִם לָהֶם וְלֹא יִרְאוּ. אָזְנָיִם לָהֶם וְלֹא יִשְׁמָעוּ, אַף לָהֶם וְלֹא יְרִיחוּן. יְדֵיהֶם וְלֹא יְמִישׁוּן, רַגְלֵיהֶם וְלֹא יְהַלֵּכוּ, לֹא יֶהְגּוּ בִּגְרוֹנָם. כְּמוֹהֶם יִהְיוּ עֹשֵׂיהֶם, כֹּל אֲשֶׁר בֹּטֵחַ בָּהֶם. יִשְׂרָאֵל בְּטַח בַּה', עֶזְרָם וּמָגִנָּם הוּא. בֵּית אַהֲרֹן בִּטְחוּ בַּה', עֶזְרָם וּמָגִנָּם הוּא. יִרְאֵי ה' בִּטְחוּ בַּה', עֶזְרָם וּמָגִנָּם הוּא.	Not to us, not to us, but rather to Your Name, give glory for your kindness and for your truth. Why should the nations say, "Say, where is their G-d?" But our G-d is in the heavens, all that He wanted, He has done. Their idols are silver and gold, the work of men's hands. They have a mouth but do not speak; they have eyes but do not see. They have ears but do not hear; they have a nose but do not smell. Hands, but they do not feel; feet, but do not walk; they do not make a peep from their throat. Like them will be their makers, all those that trust in them. Israel, trust in Hashem; their help and shield is He. House of Aharon, trust in Hashem; their help and shield is He. Those that fear Hashem, trust in Hashem; their help and shield is He.
ה' זְכָרָנוּ יְבָרֵךְ, יְבָרֵךְ אֶת בֵּית יִשְׂרָאֵל, יְבָרֵךְ אֶת בֵּית אַהֲרֹן, יְבָרֵךְ יִרְאֵי ה', הַקְּטַנִים עִם הַגְּדֹלִים. יֹסֵף ה' עֲלֵיכֶם, עֲלֵיכֶם וְעַל בְּנֵיכֶם. בְּרוּכִים אַתֶּם לַה', עֹשֵׂה שָׁמַיִם וָאָרֶץ. הַשָּׁמַיִם שָׁמַיִם לַה', וְהָאָרֶץ נָתַן לִבְנֵי אָדָם. לֹא הַמֵּתִים יְהַלְלוּ יָ-הּ וְלֹא כָּל יֹרְדֵי דוּמָה. וַאֲנַחְנוּ נְבָרֵךְ יָ-הּ מֵעַתָּה וְעַד עוֹלָם, הַלְלוּיָ-הּ.	Hashem Who remembers us, will bless; He will bless the House of Israel; He will bless the House of Aharon. He will bless those that fear Hashem, the small ones with the great ones. May Hashem bring increase to you, to you and to your children. Blessed are you to Hashem, the maker of the heavens and the earth. The heavens, are Hashem's heavens, but the earth He has given to the children of man. It is not the dead that will praise Hashem, and not those that go down to silence. But we will bless Hashem from now and forever. Hallelukah! (Psalms 115)