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Algorithms Correctness and Efficiency (COMP2038 UNMC) (FML1 23-24)
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What does the tactic 'trivial' do in Lean?
Observe the following Lean code:
open nat
example : ∀ n : ℕ, 0 ≠ succ n :=
begin
assume n h,
contradiction,
end
Why the code ends up with contradiction to conclude
the steps?
What is the congruence property of equality?
Given that half (succ (succ n)) = succ (half n)
Therefore, half 7 is
I. succ (half 5)II.
succ (half 6)III.
half (succ (succ 5))Observe the following Lean code:
example : (∃ x : A, PP x) → (∀ y : A, PP y → QQ y) → ∃ z : A , QQ z :=
begin
assume p pq,
cases p with a pa,
sorry,
apply pq,
exact pa,
end
Replace sorry with the correct Lean code.What is the special case mentioned in the example related to insertion sort in our lecture slides?
What is the result of m * n
What property does an equivalence relation have?