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, 4, 5, 6, 7, 8, 9^*	, , , , ⊢
	: , : , : , : , : , : , : , : , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
2	assumption		⊢
3	reference	13	⊢
4	reference	25	⊢
5	instantiation	10, 42, 14, 25	⊢
	: , : , :
6	reference	16	⊢
7	instantiation	11, 42, 14, 25, 15, 17, 18	, ⊢
	: , : , : , :
8	reference	19	⊢
9	instantiation	12, 13, 47, 14, 25, 15, 16, 17, 18, 19	, , , ⊢
	: , : , : , : , : , : , : , : , : , :
10	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
11	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
12	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_disassociation
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
14	instantiation	20	⊢
	: , :
15	instantiation	20	⊢
	: , :
16	assumption		⊢
17	assumption		⊢
18	modus ponens	21, 22	⊢
19	assumption		⊢
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	instantiation	23, 24, 25	⊢
	: , : , : , : , : , :
22	generalization	26	⊢
23	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
24	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
25	instantiation	27, 28	⊢
	:
26	instantiation	29, 30	, ⊢
	:
27	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
29	assumption		⊢
30	instantiation	31, 32, 33	⊢
	:
31	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
32	instantiation	48, 34, 46	⊢
	: , : , :
33	instantiation	35, 36	⊢
	: , :
34	instantiation	37, 44, 45	⊢
	: , :
35	theorem		⊢
	proveit.numbers.ordering.relax_less
36	instantiation	38, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
38	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
39	instantiation	41, 42	⊢
	:
40	instantiation	43, 44, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
44	instantiation	48, 49, 47	⊢
	: , : , :
45	instantiation	48, 49, 50	⊢
	: , : , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements