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	reference	20	⊢
2	reference	57	⊢
3	reference	22	⊢
4	reference	21	⊢
5	reference	23	⊢
6	reference	24	⊢
7	reference	47	⊢
8	instantiation	10, 24, 57, 50	, ⊢
	: , : , : , :
9	instantiation	11, 12, 13	, , ⊢
	: , : , :
10	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_closure
11	axiom		⊢
	proveit.logic.equality.equals_transitivity
12	instantiation	14, 15	, , ⊢
	: , : , :
13	instantiation	16, 17, 18, 52, 19^*	, , ⊢
	: , : , : , : , :
14	axiom		⊢
	proveit.logic.equality.substitution
15	instantiation	20, 57, 21, 22, 23, 24, 47, 50	, , ⊢
	: , : , : , : , : , : , : , : , : , :
16	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
17	instantiation	45, 25	⊢
	:
18	instantiation	48, 26, 27	, ⊢
	: , : , :
19	instantiation	28, 52, 29^*	⊢
	: , :
20	theorem		⊢
	proveit.linear_algebra.tensors.factor_scalar_from_tensor_prod
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
22	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	30, 54	⊢
	:
25	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
26	instantiation	31, 35, 32, 54, 33^*	⊢
	: , : , :
27	instantiation	34, 35, 36, 37, 38, 39, 40	, ⊢
	: , : , : , :
28	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
29	instantiation	41, 52, 42, 43^, 44^	⊢
	: , : , :
30	theorem		⊢
	proveit.linear_algebra.real_vec_set_is_vec_space
31	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
32	instantiation	46	⊢
	: , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
34	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
36	instantiation	46	⊢
	: , :
37	instantiation	45, 54	⊢
	:
38	instantiation	46	⊢
	: , :
39	instantiation	48, 49, 47	⊢
	: , : , :
40	instantiation	48, 49, 50	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
43	instantiation	51, 52	⊢
	:
44	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
45	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
47	assumption		⊢
48	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
49	instantiation	53, 54, 55	⊢
	: , : , :
50	assumption		⊢
51	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
52	instantiation	56, 59, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
55	instantiation	58, 59	⊢
	: , :
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	assumption		⊢
58	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
^*equality replacement requirements