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, 43, 6, 7, 8, 9	⊢
	: , : , : , : , : , : , : , : , : , :
4	generalization	10	, , , ⊢
5	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_distribution_over_summation
6	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
8	instantiation	11, 14, 15, 16	⊢
	: , : , :
9	instantiation	12	⊢
	: , :
10	instantiation	13, 14, 15, 16, 17, 18, 19, 20, 21	, , , , ⊢
	: , : , : , :
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
14	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
15	instantiation	24	⊢
	: , : , : , :
16	instantiation	22, 23	⊢
	:
17	instantiation	24	⊢
	: , : , : , :
18	assumption		⊢
19	assumption		⊢
20	instantiation	25, 26	, ⊢
	:
21	assumption		⊢
22	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
23	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
25	assumption		⊢
26	instantiation	27, 28, 29	⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
28	instantiation	44, 30, 42	⊢
	: , : , :
29	instantiation	31, 32	⊢
	: , :
30	instantiation	33, 40, 41	⊢
	: , :
31	theorem		⊢
	proveit.numbers.ordering.relax_less
32	instantiation	34, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
34	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
35	instantiation	37, 38	⊢
	:
36	instantiation	39, 40, 41, 42	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
39	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
40	instantiation	44, 45, 43	⊢
	: , : , :
41	instantiation	44, 45, 46	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat4