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