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	4	⊢
2	instantiation	4, 5, 6	⊢
	: , : , :
3	instantiation	7, 8, 9	⊢
	: , : , :
4	theorem		⊢
	proveit.logic.equality.sub_right_side_into
5	instantiation	10, 23, 25, 11, 12, 13	⊢
	: , : , : , : , :
6	instantiation	20, 14	⊢
	: , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	20, 15	⊢
	: , : , :
9	instantiation	31, 16	⊢
	:
10	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_denom_left
11	instantiation	73, 19, 17	⊢
	: , : , :
12	instantiation	73, 19, 18	⊢
	: , : , :
13	instantiation	73, 19, 39	⊢
	: , : , :
14	instantiation	20, 21	⊢
	: , : , :
15	instantiation	22, 23	⊢
	:
16	instantiation	24, 25, 26, 27	⊢
	: , :
17	instantiation	73, 29, 28	⊢
	: , : , :
18	instantiation	73, 29, 30	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
20	axiom		⊢
	proveit.logic.equality.substitution
21	instantiation	31, 32	⊢
	:
22	theorem		⊢
	proveit.numbers.division.frac_one_denom
23	instantiation	73, 74, 33	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.div_complex_closure
25	instantiation	34, 35, 36	⊢
	: , :
26	instantiation	73, 74, 37	⊢
	: , : , :
27	instantiation	38, 39	⊢
	:
28	instantiation	73, 41, 40	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
30	instantiation	73, 41, 42	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
32	instantiation	73, 74, 43	⊢
	: , : , :
33	instantiation	73, 55, 44	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
35	instantiation	73, 74, 45	⊢
	: , : , :
36	instantiation	73, 74, 46	⊢
	: , : , :
37	instantiation	73, 57, 48	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
39	instantiation	73, 47, 48	⊢
	: , : , :
40	instantiation	73, 50, 49	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
42	instantiation	73, 50, 53	⊢
	: , : , :
43	instantiation	51, 52, 53	⊢
	: , : , :
44	instantiation	73, 64, 54	⊢
	: , : , :
45	instantiation	73, 55, 56	⊢
	: , : , :
46	instantiation	73, 57, 60	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
48	instantiation	58, 59, 60	⊢
	: , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
51	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
52	instantiation	61, 62	⊢
	: , :
53	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
54	instantiation	73, 68, 63	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
56	instantiation	73, 64, 65	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
58	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
60	instantiation	66, 67	⊢
	:
61	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	73, 68, 69	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
67	instantiation	70, 71, 72	⊢
	:
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
70	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
71	instantiation	73, 74, 75	⊢
	: , : , :
72	assumption		⊢
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
75	instantiation	76, 77	⊢
	:
76	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
77	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int