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	71	⊢
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
3	instantiation	4, 5	⊢
	:
4	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
5	instantiation	6, 7, 8	⊢
	: , :
6	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
7	instantiation	71, 36, 49	⊢
	: , : , :
8	instantiation	9, 10	⊢
	:
9	theorem		⊢
	proveit.numbers.negation.complex_closure
10	instantiation	11, 12, 13	⊢
	: , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
12	instantiation	71, 36, 14	⊢
	: , : , :
13	instantiation	15, 16, 17	⊢
	: , : , :
14	instantiation	71, 45, 18	⊢
	: , : , :
15	theorem		⊢
	proveit.logic.equality.sub_right_side_into
16	instantiation	23, 24, 19	⊢
	: , :
17	instantiation	20, 21, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
19	instantiation	23, 32, 33	⊢
	: , :
20	axiom		⊢
	proveit.logic.equality.equals_transitivity
21	instantiation	25, 70, 57, 26, 29, 27, 24, 32, 33	⊢
	: , : , : , : , : , :
22	instantiation	25, 26, 57, 27, 28, 29, 30, 31, 32, 33	⊢
	: , : , : , : , : , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
24	instantiation	71, 36, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.disassociation
26	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
27	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
28	instantiation	35	⊢
	: , :
29	instantiation	35	⊢
	: , :
30	instantiation	71, 36, 39	⊢
	: , : , :
31	instantiation	71, 36, 40	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
33	instantiation	71, 36, 37	⊢
	: , : , :
34	instantiation	38, 39, 40	⊢
	: , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	instantiation	41, 42, 43	⊢
	: , :
38	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
39	instantiation	71, 55, 44	⊢
	: , : , :
40	instantiation	71, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
42	instantiation	47, 48, 49, 50	⊢
	: , : , :
43	instantiation	51, 52	⊢
	:
44	instantiation	71, 58, 53	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
49	instantiation	71, 55, 54	⊢
	: , : , :
50	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
51	theorem		⊢
	proveit.numbers.negation.real_closure
52	instantiation	71, 55, 56	⊢
	: , : , :
53	instantiation	71, 69, 57	⊢
	: , : , :
54	instantiation	71, 58, 66	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	71, 58, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	71, 60, 61	⊢
	: , : , :
60	instantiation	62, 63, 68	⊢
	: , :
61	assumption		⊢
62	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
63	instantiation	64, 65, 66	⊢
	: , :
64	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
65	instantiation	67, 68	⊢
	:
66	instantiation	71, 69, 70	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.negation.int_closure
68	instantiation	71, 72, 73	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
73	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos