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	73	⊢
2	reference	38	⊢
3	instantiation	73, 4, 5	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
5	instantiation	6, 7	⊢
	:
6	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
7	instantiation	8, 9, 10	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
9	instantiation	73, 38, 51	⊢
	: , : , :
10	instantiation	11, 12	⊢
	:
11	theorem		⊢
	proveit.numbers.negation.complex_closure
12	instantiation	13, 14, 15	⊢
	: , :
13	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
14	instantiation	73, 38, 16	⊢
	: , : , :
15	instantiation	17, 18, 19	⊢
	: , : , :
16	instantiation	73, 47, 20	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.equality.sub_right_side_into
18	instantiation	25, 26, 21	⊢
	: , :
19	instantiation	22, 23, 24	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
21	instantiation	25, 34, 35	⊢
	: , :
22	axiom		⊢
	proveit.logic.equality.equals_transitivity
23	instantiation	27, 72, 59, 28, 31, 29, 26, 34, 35	⊢
	: , : , : , : , : , :
24	instantiation	27, 28, 59, 29, 30, 31, 32, 33, 34, 35	⊢
	: , : , : , : , : , :
25	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
26	instantiation	73, 38, 36	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.disassociation
28	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
29	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
30	instantiation	37	⊢
	: , :
31	instantiation	37	⊢
	: , :
32	instantiation	73, 38, 41	⊢
	: , : , :
33	instantiation	73, 38, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
35	instantiation	73, 38, 39	⊢
	: , : , :
36	instantiation	40, 41, 42	⊢
	: , :
37	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	43, 44, 45	⊢
	: , :
40	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
41	instantiation	73, 57, 46	⊢
	: , : , :
42	instantiation	73, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
44	instantiation	49, 50, 51, 52	⊢
	: , : , :
45	instantiation	53, 54	⊢
	:
46	instantiation	73, 60, 55	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
48	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
51	instantiation	73, 57, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
53	theorem		⊢
	proveit.numbers.negation.real_closure
54	instantiation	73, 57, 58	⊢
	: , : , :
55	instantiation	73, 71, 59	⊢
	: , : , :
56	instantiation	73, 60, 68	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
58	instantiation	73, 60, 61	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
60	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
61	instantiation	73, 62, 63	⊢
	: , : , :
62	instantiation	64, 65, 70	⊢
	: , :
63	assumption		⊢
64	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
65	instantiation	66, 67, 68	⊢
	: , :
66	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
67	instantiation	69, 70	⊢
	:
68	instantiation	73, 71, 72	⊢
	: , : , :
69	theorem		⊢
	proveit.numbers.negation.int_closure
70	instantiation	73, 74, 75	⊢
	: , : , :
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
75	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos