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	⊢
	: , : , :
1	reference	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8, 9	⊢
	: , :
4	axiom		⊢
	proveit.logic.equality.equals_transitivity
5	instantiation	32, 15	⊢
	: , : , :
6	instantiation	32, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
8	instantiation	11, 12, 13	⊢
	: , :
9	instantiation	14	⊢
	:
10	instantiation	32, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
12	instantiation	16, 25, 17, 18	⊢
	: , :
13	instantiation	75, 47, 19	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_reflexivity
15	instantiation	20, 21, 22, 23	⊢
	: , : , : , :
16	theorem		⊢
	proveit.numbers.division.div_complex_closure
17	instantiation	24, 40, 25	⊢
	: , :
18	instantiation	26, 41, 27	⊢
	: , : , :
19	instantiation	53, 54, 28	⊢
	: , : , :
20	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
21	instantiation	32, 29	⊢
	: , : , :
22	instantiation	30, 31	⊢
	: , :
23	instantiation	32, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
25	instantiation	75, 47, 34	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.equality.sub_left_side_into
27	instantiation	35, 40	⊢
	:
28	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
29	instantiation	36, 37, 38	⊢
	: , :
30	theorem		⊢
	proveit.logic.equality.equals_reversal
31	instantiation	39, 40, 46, 45, 41	⊢
	: , : , :
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	42, 43, 79	⊢
	: , :
34	instantiation	75, 58, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
36	theorem		⊢
	proveit.numbers.addition.commutation
37	instantiation	75, 47, 45	⊢
	: , : , :
38	instantiation	75, 47, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
40	instantiation	75, 47, 48	⊢
	: , : , :
41	instantiation	49, 77	⊢
	:
42	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
43	instantiation	75, 50, 51	⊢
	: , : , :
44	instantiation	75, 67, 52	⊢
	: , : , :
45	instantiation	53, 54, 55	⊢
	: , : , :
46	instantiation	75, 56, 57	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	75, 58, 59	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
50	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
51	instantiation	75, 60, 61	⊢
	: , : , :
52	instantiation	75, 73, 62	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
54	instantiation	63, 64	⊢
	: , :
55	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
57	instantiation	75, 65, 66	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	75, 67, 68	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
61	instantiation	75, 69, 70	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
66	instantiation	75, 71, 72	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
68	instantiation	75, 73, 74	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
70	instantiation	75, 76, 77	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
72	instantiation	78, 79	⊢
	:
73	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
74	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
78	theorem		⊢
	proveit.numbers.negation.int_neg_closure
79	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1