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	theorem		⊢
	proveit.logic.equality.sub_right_side_into
2	instantiation	42, 4	⊢
	: , :
3	instantiation	5, 20, 6, 7, 8^, 9^	⊢
	: , : , : , :
4	instantiation	10, 11, 12, 13, 14, 15	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.division.prod_of_fracs
6	instantiation	94, 17, 16	⊢
	: , : , :
7	instantiation	94, 17, 18	⊢
	: , : , :
8	instantiation	19, 20	⊢
	:
9	instantiation	21, 75, 86, 73, 61^*	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
11	instantiation	94, 90, 22	⊢
	: , : , :
12	instantiation	23, 26	⊢
	: , :
13	instantiation	94, 90, 24	⊢
	: , : , :
14	instantiation	25, 26, 27, 28, 29	⊢
	: , : , :
15	instantiation	62, 34	⊢
	:
16	instantiation	94, 31, 30	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
18	instantiation	94, 31, 32	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
20	instantiation	94, 84, 57	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
22	instantiation	33, 35, 36	⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
24	instantiation	94, 48, 34	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
26	instantiation	94, 90, 35	⊢
	: , : , :
27	instantiation	94, 90, 36	⊢
	: , : , :
28	instantiation	37, 38, 39, 40, 41	⊢
	: , : , :
29	instantiation	42, 43	⊢
	: , :
30	instantiation	94, 45, 44	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
32	instantiation	94, 45, 46	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.multiplication.mult_rational_closure_bin
34	instantiation	76, 77, 47	⊢
	: , :
35	instantiation	94, 48, 63	⊢
	: , : , :
36	instantiation	49, 69, 50, 51	⊢
	: , :
37	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
38	instantiation	94, 52, 53	⊢
	: , : , :
39	instantiation	94, 54, 78	⊢
	: , : , :
40	instantiation	94, 54, 55	⊢
	: , : , :
41	instantiation	56, 85, 57, 58, 59, 60, 61^*	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.ordering.relax_less
43	instantiation	62, 63	⊢
	:
44	instantiation	94, 64, 88	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
46	instantiation	94, 64, 80	⊢
	: , : , :
47	instantiation	94, 87, 65	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_pos_within_rational
49	theorem		⊢
	proveit.numbers.division.div_rational_closure
50	instantiation	94, 92, 66	⊢
	: , : , :
51	instantiation	67, 80	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
53	instantiation	94, 68, 89	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
55	instantiation	94, 87, 80	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.exponentiation.exp_monotonicity_large_base_less_eq
57	instantiation	94, 90, 69	⊢
	: , : , :
58	instantiation	70, 71, 73	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.numerals.decimals.less_1_2
60	instantiation	72, 73	⊢
	:
61	instantiation	74, 75	⊢
	:
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.positive_if_in_rational_pos
63	instantiation	76, 77, 78	⊢
	: , :
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
65	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
66	instantiation	94, 79, 80	⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
68	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
69	instantiation	94, 92, 81	⊢
	: , : , :
70	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
71	instantiation	82, 83	⊢
	: , :
72	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
73	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
74	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
75	instantiation	94, 84, 85	⊢
	: , : , :
76	theorem		⊢
	proveit.numbers.division.div_rational_pos_closure
77	instantiation	94, 87, 86	⊢
	: , : , :
78	instantiation	94, 87, 88	⊢
	: , : , :
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
80	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
81	instantiation	94, 95, 89	⊢
	: , : , :
82	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
83	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
84	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
85	instantiation	94, 90, 91	⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
87	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
88	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
89	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
90	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
91	instantiation	94, 92, 93	⊢
	: , : , :
92	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
93	instantiation	94, 95, 96	⊢
	: , : , :
94	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
95	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
96	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements