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