Proof of proveit.logic.booleans.conjunction.unary_and_reduction_lemma theorem

import proveit
from proveit.numbers import num
from proveit import A, B, m
from proveit.logic.booleans.conjunction  import multi_conjunction_def
theory = proveit.Theory() # the theorem's theory

%proving unary_and_reduction_lemma

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
unary_and_reduction_lemma:
(see dependencies)

multi_conjunction_def

 ⊢  

multi_conjunction_def.instantiate({m:num(0), A:(), B:A})

 ⊢  

unary_and_reduction_lemma may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".

%qed

proveit.logic.booleans.conjunction.unary_and_reduction_lemma has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4, 5*	⊢
	: , : , :
2	axiom		⊢
	proveit.logic.booleans.conjunction.multi_conjunction_def
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	conjecture		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	theorem		⊢
	proveit.logic.booleans.conjunction.empty_conjunction_eval
*equality replacement requirements