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, 3	, , , , ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	9, 4	, , , , ⊢
	: , :
3	instantiation	5, 6	, , , ⊢
	: , : , :
4	modus ponens	7, 8	, , , , ⊢
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	9, 10	, , , ⊢
	: , :
7	instantiation	11, 18, 20, 12	⊢
	: , : , : , : , : , : , :
8	modus ponens	13, 15	, , , ⊢
9	theorem		⊢
	proveit.logic.equality.equals_reversal
10	modus ponens	14, 15	, , , ⊢
11	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
12	assumption		⊢
13	instantiation	16, 18, 20	⊢
	: , : , : , : , : , :
14	instantiation	17, 55, 18, 19, 20, 21	⊢
	: , : , : , : , : , : , : , : , : , :
15	generalization	22	, , , ⊢
16	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
17	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
20	instantiation	23, 26, 27, 28	⊢
	: , : , :
21	instantiation	24	⊢
	: , :
22	instantiation	25, 26, 27, 28, 29, 30, 31, 32, 33	, , , , ⊢
	: , : , : , :
23	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
26	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
27	instantiation	36	⊢
	: , : , : , :
28	instantiation	34, 35	⊢
	:
29	instantiation	36	⊢
	: , : , : , :
30	assumption		⊢
31	assumption		⊢
32	instantiation	37, 38	, ⊢
	:
33	assumption		⊢
34	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
36	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
37	assumption		⊢
38	instantiation	39, 40, 41	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
40	instantiation	56, 42, 54	⊢
	: , : , :
41	instantiation	43, 44	⊢
	: , :
42	instantiation	45, 52, 53	⊢
	: , :
43	theorem		⊢
	proveit.numbers.ordering.relax_less
44	instantiation	46, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
46	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
47	instantiation	49, 50	⊢
	:
48	instantiation	51, 52, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
50	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
51	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
52	instantiation	56, 57, 55	⊢
	: , : , :
53	instantiation	56, 57, 58	⊢
	: , : , :
54	assumption		⊢
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.nat4