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^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_subtract
2	reference	88	⊢
3	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	reference	60	⊢
6	instantiation	86, 62, 9	⊢
	: , : , :
7	instantiation	10, 34, 60, 28	⊢
	: , :
8	instantiation	13, 11, 12	⊢
	: , : , :
9	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
10	theorem		⊢
	proveit.numbers.division.div_complex_closure
11	instantiation	13, 14, 15	⊢
	: , : , :
12	instantiation	16, 17, 18, 19	⊢
	: , : , : , :
13	theorem		⊢
	proveit.logic.equality.sub_right_side_into
14	instantiation	20, 33, 34, 21, 22	⊢
	: , : , : , : , :
15	instantiation	40, 23, 24	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
17	instantiation	50, 25	⊢
	: , : , :
18	instantiation	50, 26	⊢
	: , : , :
19	instantiation	59, 34	⊢
	:
20	theorem		⊢
	proveit.numbers.division.mult_frac_cancel_numer_left
21	instantiation	27, 60, 28	⊢
	:
22	instantiation	86, 29, 30	⊢
	: , : , :
23	instantiation	50, 31	⊢
	: , : , :
24	instantiation	50, 32	⊢
	: , : , :
25	instantiation	52, 33	⊢
	:
26	instantiation	52, 34	⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
28	instantiation	35, 36, 37	⊢
	: , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
30	instantiation	86, 38, 39	⊢
	: , : , :
31	instantiation	40, 41, 42	⊢
	: , : , :
32	instantiation	50, 43	⊢
	: , : , :
33	instantiation	86, 62, 44	⊢
	: , : , :
34	instantiation	86, 62, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
36	instantiation	86, 48, 46	⊢
	: , : , :
37	instantiation	86, 48, 47	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
39	instantiation	86, 48, 49	⊢
	: , : , :
40	axiom		⊢
	proveit.logic.equality.equals_transitivity
41	instantiation	50, 51	⊢
	: , : , :
42	instantiation	52, 60	⊢
	:
43	instantiation	53, 60	⊢
	:
44	instantiation	86, 67, 54	⊢
	: , : , :
45	instantiation	86, 67, 55	⊢
	: , : , :
46	instantiation	86, 57, 56	⊢
	: , : , :
47	instantiation	86, 57, 85	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
49	instantiation	86, 57, 58	⊢
	: , : , :
50	axiom		⊢
	proveit.logic.equality.substitution
51	instantiation	59, 60	⊢
	:
52	theorem		⊢
	proveit.numbers.division.frac_one_denom
53	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
54	instantiation	86, 71, 82	⊢
	: , : , :
55	instantiation	86, 71, 61	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
58	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
59	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
60	instantiation	86, 62, 63	⊢
	: , : , :
61	instantiation	64, 65, 66	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
63	instantiation	86, 67, 68	⊢
	: , : , :
64	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
65	instantiation	69, 70	⊢
	: , :
66	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_in_m_domain
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
68	instantiation	86, 71, 76	⊢
	: , : , :
69	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
70	instantiation	72, 73, 74	⊢
	: , :
71	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
72	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
73	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
74	instantiation	75, 76, 77	⊢
	: , :
75	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
76	instantiation	78, 79, 80	⊢
	: , :
77	instantiation	81, 82	⊢
	:
78	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
79	instantiation	86, 87, 83	⊢
	: , : , :
80	instantiation	86, 84, 85	⊢
	: , : , :
81	theorem		⊢
	proveit.numbers.negation.int_closure
82	instantiation	86, 87, 88	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
84	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
85	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
86	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
87	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
88	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements