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