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	generalization	1	, , , ⊢
1	instantiation	26, 2, 3	, , , , ⊢
	: , : , :
2	instantiation	4, 70, 5, 6, 7, 8	, , , , ⊢
	: , : , : , :
3	instantiation	10, 11, 12, 14, 35, 9^*	, , , , ⊢
	: , : , : , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	instantiation	49	⊢
	: , :
6	instantiation	49	⊢
	: , :
7	instantiation	24, 41, 42	, ⊢
	: , :
8	instantiation	10, 11, 12, 47, 48, 13^*	, , , ⊢
	: , : , : , : , :
9	instantiation	24, 14, 35, 15^*	, , ⊢
	: , :
10	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.doubly_scaled_as_singly_scaled
11	instantiation	16, 18, 19, 20	⊢
	: , : , :
12	instantiation	17, 18, 19, 20, 21, 22, 23	, ⊢
	: , : , : , :
13	instantiation	24, 47, 48	, ⊢
	: , :
14	instantiation	71, 53, 25	, ⊢
	: , : , :
15	instantiation	26, 27, 28	, , ⊢
	: , : , :
16	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_vec_spaces_is_vec_space
17	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_is_in_tensor_prod_space
18	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
19	instantiation	49	⊢
	: , :
20	instantiation	29, 44	⊢
	:
21	instantiation	49	⊢
	: , :
22	instantiation	31, 32, 30	⊢
	: , : , :
23	instantiation	31, 32, 33	⊢
	: , : , :
24	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
25	instantiation	34, 50, 56	, ⊢
	: , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	36, 37, 70, 66, 40, 38, 41, 42, 35	, , ⊢
	: , : , : , : , : , :
28	instantiation	36, 70, 37, 38, 39, 40, 41, 42, 47, 48	, , ⊢
	: , : , : , : , : , :
29	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
30	assumption		⊢
31	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
32	instantiation	43, 44, 45	⊢
	: , : , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
35	instantiation	46, 47, 48	, ⊢
	: , :
36	theorem		⊢
	proveit.numbers.multiplication.disassociation
37	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
38	instantiation	49	⊢
	: , :
39	instantiation	49	⊢
	: , :
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	71, 53, 50	⊢
	: , : , :
42	instantiation	71, 53, 56	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.cartesian_products.cart_exp_subset_eq
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat3
45	instantiation	51, 53	⊢
	: , :
46	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
47	instantiation	71, 53, 52	⊢
	: , : , :
48	instantiation	71, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	assumption		⊢
51	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
52	assumption		⊢
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	55, 56, 57	⊢
	: , :
55	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
56	instantiation	71, 59, 58	⊢
	: , : , :
57	instantiation	71, 59, 60	⊢
	: , : , :
58	instantiation	71, 62, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
60	instantiation	71, 62, 63	⊢
	: , : , :
61	instantiation	71, 64, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	instantiation	71, 72, 66	⊢
	: , : , :
64	instantiation	67, 68, 69	⊢
	: , :
65	assumption		⊢
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
68	instantiation	71, 72, 70	⊢
	: , : , :
69	instantiation	71, 72, 73	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements