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^*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.division.frac_cancel_left
2	instantiation	86, 5, 6	⊢
	: , : , :
3	reference	57	⊢
4	instantiation	35, 7, 8	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
6	instantiation	86, 9, 10	⊢
	: , : , :
7	instantiation	11, 76, 12, 13, 14, 15	⊢
	: , : , : , :
8	instantiation	51, 16	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
10	instantiation	17, 18, 19	⊢
	: , :
11	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
12	instantiation	20	⊢
	: , :
13	instantiation	20	⊢
	: , :
14	instantiation	21, 34, 57	⊢
	: , :
15	instantiation	22, 34, 48, 23^, 24^	⊢
	: , : , :
16	instantiation	25, 26, 27, 28	⊢
	: , : , : , :
17	theorem		⊢
	proveit.numbers.addition.add_real_pos_closure_bin
18	instantiation	86, 41, 29	⊢
	: , : , :
19	instantiation	30, 31, 32, 58	⊢
	: , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
21	theorem		⊢
	proveit.numbers.multiplication.commutation
22	theorem		⊢
	proveit.numbers.exponentiation.product_of_posnat_powers
23	instantiation	33, 34	⊢
	:
24	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
25	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
26	instantiation	35, 36, 37	⊢
	: , : , :
27	instantiation	38	⊢
	:
28	instantiation	39, 45	⊢
	: , :
29	instantiation	86, 47, 40	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
31	instantiation	86, 41, 42	⊢
	: , : , :
32	instantiation	43, 73, 67	⊢
	:
33	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
34	instantiation	86, 74, 44	⊢
	: , : , :
35	axiom		⊢
	proveit.logic.equality.equals_transitivity
36	instantiation	51, 45	⊢
	: , : , :
37	instantiation	63, 46	⊢
	:
38	axiom		⊢
	proveit.logic.equality.equals_reflexivity
39	theorem		⊢
	proveit.logic.equality.equals_reversal
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
42	instantiation	86, 47, 48	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
44	instantiation	49, 60, 50	⊢
	: , :
45	instantiation	51, 52	⊢
	: , : , :
46	instantiation	53, 54, 64	⊢
	: , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
48	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
49	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
50	instantiation	55, 81, 73, 58	⊢
	: , :
51	axiom		⊢
	proveit.logic.equality.substitution
52	instantiation	56, 57, 69, 58, 59^*	⊢
	: , :
53	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
54	instantiation	86, 74, 60	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.division.div_real_closure
56	theorem		⊢
	proveit.numbers.division.div_as_mult
57	instantiation	86, 74, 81	⊢
	: , : , :
58	instantiation	61, 62	⊢
	: , :
59	instantiation	63, 64	⊢
	:
60	instantiation	86, 82, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
62	instantiation	66, 78, 73, 67	⊢
	: , :
63	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
64	instantiation	68, 69, 70	⊢
	: , :
65	instantiation	86, 84, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
67	instantiation	72, 78, 81, 79	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
69	instantiation	86, 74, 73	⊢
	: , : , :
70	instantiation	86, 74, 75	⊢
	: , : , :
71	instantiation	86, 87, 76	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
73	instantiation	77, 78, 81, 79	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
75	instantiation	80, 81	⊢
	:
76	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
77	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
79	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
80	theorem		⊢
	proveit.numbers.negation.real_closure
81	instantiation	86, 82, 83	⊢
	: , : , :
82	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
83	instantiation	86, 84, 85	⊢
	: , : , :
84	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
85	instantiation	86, 87, 88	⊢
	: , : , :
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