Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2	, , , , ⊢
	: , :
1	theorem		⊢
	proveit.logic.equality.equals_reversal
2	modus ponens	3, 4	, , , , ⊢
3	instantiation	5, 10, 11, 6	⊢
	: , : , : , : , : , : , :
4	modus ponens	7, 8	, , , ⊢
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
6	assumption		⊢
7	instantiation	9, 10, 11	⊢
	: , : , : , : , : , :
8	generalization	12	, , , ⊢
9	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
11	instantiation	13, 15, 16, 17	⊢
	: , : , :
12	instantiation	14, 15, 16, 17, 18, 19, 20, 21, 22	, , , , ⊢
	: , : , : , :
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
14	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
15	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
16	instantiation	25	⊢
	: , : , : , :
17	instantiation	23, 24	⊢
	:
18	instantiation	25	⊢
	: , : , : , :
19	assumption		⊢
20	assumption		⊢
21	instantiation	26, 27	, ⊢
	:
22	assumption		⊢
23	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
26	assumption		⊢
27	instantiation	28, 29, 30	⊢
	:
28	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
29	instantiation	45, 31, 43	⊢
	: , : , :
30	instantiation	32, 33	⊢
	: , :
31	instantiation	34, 41, 42	⊢
	: , :
32	theorem		⊢
	proveit.numbers.ordering.relax_less
33	instantiation	35, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
35	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
36	instantiation	38, 39	⊢
	:
37	instantiation	40, 41, 42, 43	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
41	instantiation	45, 46, 44	⊢
	: , : , :
42	instantiation	45, 46, 47	⊢
	: , : , :
43	assumption		⊢
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat4