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, 11, 12, 4	, ⊢
	: , : , : , : , : , : , :
2	modus ponens	5, 6	, , ⊢
3	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.distribution_over_vec_sum
4	instantiation	7, 8, 9	, ⊢
	: , : , :
5	instantiation	10, 11, 12	⊢
	: , : , : , : , : , :
6	generalization	13	, , ⊢
7	theorem		⊢
	proveit.logic.equality.sub_left_side_into
8	instantiation	14, 26, 28	, ⊢
	: , :
9	instantiation	15, 16, 17	, ⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.addition.summation_closure
11	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
12	instantiation	18, 30, 20, 21	⊢
	: , : , :
13	instantiation	19, 30, 20, 21, 22, 23, 24, 25	, , , ⊢
	: , : , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
15	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
16	instantiation	51, 27, 26	⊢
	: , : , :
17	instantiation	51, 27, 28	⊢
	: , : , :
18	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
19	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
20	instantiation	31	⊢
	: , : , :
21	instantiation	29, 30	⊢
	:
22	instantiation	31	⊢
	: , : , :
23	assumption		⊢
24	instantiation	32, 33	, ⊢
	:
25	assumption		⊢
26	assumption		⊢
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
28	assumption		⊢
29	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	assumption		⊢
33	instantiation	34, 35, 36	⊢
	:
34	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
35	instantiation	51, 37, 49	⊢
	: , : , :
36	instantiation	38, 39	⊢
	: , :
37	instantiation	40, 47, 48	⊢
	: , :
38	theorem		⊢
	proveit.numbers.ordering.relax_less
39	instantiation	41, 42, 43	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
42	instantiation	44, 45	⊢
	:
43	instantiation	46, 47, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
46	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
47	instantiation	51, 52, 50	⊢
	: , : , :
48	instantiation	51, 52, 53	⊢
	: , : , :
49	assumption		⊢
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat4