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, 4, 5, 6, 7, 8, 9, 10, 11	⊢
	: , : , : , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_general
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	55	⊢
4	reference	65	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	12	⊢
	: , :
7	instantiation	13, 14, 15	⊢
	: , :
8	instantiation	63, 43, 16	⊢
	: , : , :
9	reference	27	⊢
10	instantiation	17, 18	⊢
	:
11	instantiation	19	⊢
	:
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
13	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
14	instantiation	20, 27, 21, 22	⊢
	: , :
15	instantiation	26, 37, 23	⊢
	: , :
16	instantiation	63, 49, 24	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.negation.complex_closure
18	instantiation	63, 43, 25	⊢
	: , : , :
19	axiom		⊢
	proveit.logic.equality.equals_reflexivity
20	theorem		⊢
	proveit.numbers.division.div_complex_closure
21	instantiation	26, 37, 27	⊢
	: , :
22	instantiation	28, 29, 30	⊢
	: , : , :
23	instantiation	63, 43, 31	⊢
	: , : , :
24	instantiation	63, 54, 58	⊢
	: , : , :
25	instantiation	63, 49, 32	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
27	instantiation	63, 43, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.logic.equality.sub_left_side_into
29	instantiation	34, 35	⊢
	:
30	instantiation	36, 37	⊢
	:
31	instantiation	38, 39, 40	⊢
	: , : , :
32	instantiation	63, 54, 41	⊢
	: , : , :
33	instantiation	63, 49, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
35	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
36	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
37	instantiation	63, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
39	instantiation	45, 46	⊢
	: , :
40	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
41	instantiation	63, 47, 48	⊢
	: , : , :
42	instantiation	63, 54, 52	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
44	instantiation	63, 49, 50	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
47	instantiation	51, 52, 53	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	63, 54, 62	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
52	instantiation	63, 64, 55	⊢
	: , : , :
53	instantiation	56, 57, 58	⊢
	: , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
56	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
57	instantiation	63, 59, 60	⊢
	: , : , :
58	instantiation	61, 62	⊢
	:
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
60	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
61	theorem		⊢
	proveit.numbers.negation.int_closure
62	instantiation	63, 64, 65	⊢
	: , : , :
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat2