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	4, 5, 6, 7, 8	⊢
	: , : , : , : , :
3	instantiation	26, 9, 10	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
5	instantiation	68, 49, 11	⊢
	: , : , :
6	instantiation	68, 49, 12	⊢
	: , : , :
7	instantiation	13, 46, 14	⊢
	:
8	instantiation	68, 15, 16	⊢
	: , : , :
9	instantiation	35, 17	⊢
	: , : , :
10	instantiation	35, 18	⊢
	: , : , :
11	instantiation	68, 54, 19	⊢
	: , : , :
12	instantiation	68, 54, 20	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
14	instantiation	21, 22, 23	⊢
	: , :
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
16	instantiation	68, 24, 25	⊢
	: , : , :
17	instantiation	26, 27, 28	⊢
	: , : , :
18	instantiation	35, 29	⊢
	: , : , :
19	instantiation	68, 58, 61	⊢
	: , : , :
20	instantiation	68, 58, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
22	instantiation	68, 33, 31	⊢
	: , : , :
23	instantiation	68, 33, 32	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
25	instantiation	68, 33, 34	⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.equals_transitivity
27	instantiation	35, 36	⊢
	: , : , :
28	instantiation	37, 46	⊢
	:
29	instantiation	38, 46	⊢
	:
30	instantiation	39, 40, 41	⊢
	: , : , :
31	instantiation	68, 43, 42	⊢
	: , : , :
32	instantiation	68, 43, 70	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34	instantiation	68, 43, 44	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.substitution
36	instantiation	45, 46	⊢
	:
37	theorem		⊢
	proveit.numbers.division.frac_one_denom
38	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
39	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
40	instantiation	47, 48	⊢
	: , :
41	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_in_m_domain
42	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
45	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
46	instantiation	68, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
48	instantiation	51, 52, 53	⊢
	: , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	68, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
52	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
53	instantiation	56, 59, 57	⊢
	: , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	68, 58, 59	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
57	instantiation	60, 61	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
59	instantiation	62, 63, 64	⊢
	: , :
60	theorem		⊢
	proveit.numbers.negation.int_closure
61	instantiation	68, 66, 65	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
63	instantiation	68, 66, 67	⊢
	: , : , :
64	instantiation	68, 69, 70	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
66	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
70	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos