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$\begingroup$ Perhaps it's our naming convention that confuses you: since we don't care which element of these types we have, we just name an element after the type, instead of giving names according to the structure of the element. $\endgroup$ – Trebor ♦ Commented May 21 at 8:57 -
$\begingroup$ You have two judgements here: the first one is that add_mul : ∀ (a b c : ℕ), (a + b) * c = a * c + b * c and the second one is that ∀ (a b c : ℕ), (a + b) * c = a * c + b * c : Prop $\endgroup$ – Agnishom Chattopadhyay Commented May 21 at 13:30
1 Answer
def cat : ∀ (a b c : ℕ), (a + b) * c = a * c + b * c := by ... def dog : Prop := ∀ (a b c : ℕ), (a + b) * c = a * c + b * c