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	reference	5	⊢
2	instantiation	5, 6, 7, 8	⊢
	: , : , : , :
3	instantiation	26, 9	⊢
	: , : , :
4	instantiation	12, 10	⊢
	: , :
5	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
6	instantiation	26, 11	⊢
	: , : , :
7	instantiation	12, 13	⊢
	: , :
8	instantiation	26, 14	⊢
	: , : , :
9	instantiation	26, 36	⊢
	: , : , :
10	instantiation	15, 29, 46, 40, 16^*	⊢
	: , :
11	instantiation	17, 18, 19	⊢
	: , :
12	theorem		⊢
	proveit.logic.equality.equals_reversal
13	instantiation	20, 46, 25, 24, 40	⊢
	: , : , :
14	instantiation	34, 35, 62	⊢
	: , :
15	theorem		⊢
	proveit.numbers.division.div_as_mult
16	instantiation	21, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.addition.commutation
18	instantiation	73, 56, 24	⊢
	: , : , :
19	instantiation	73, 56, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	26, 27	⊢
	: , : , :
23	instantiation	28, 29, 30	⊢
	: , :
24	instantiation	47, 48, 31	⊢
	: , : , :
25	instantiation	73, 32, 33	⊢
	: , : , :
26	axiom		⊢
	proveit.logic.equality.substitution
27	instantiation	34, 35, 62, 36^*	⊢
	: , :
28	theorem		⊢
	proveit.numbers.multiplication.commutation
29	instantiation	73, 56, 37	⊢
	: , : , :
30	instantiation	38, 39, 46, 40	⊢
	: , :
31	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_neg_within_real
33	instantiation	73, 41, 42	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
35	instantiation	73, 43, 44	⊢
	: , : , :
36	instantiation	45, 46	⊢
	:
37	instantiation	47, 48, 49	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.division.div_complex_closure
39	instantiation	73, 56, 50	⊢
	: , : , :
40	instantiation	51, 69	⊢
	:
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_neg_within_real_neg
42	instantiation	73, 52, 53	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
44	instantiation	73, 54, 55	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
46	instantiation	73, 56, 57	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
48	instantiation	58, 59	⊢
	: , :
49	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
50	instantiation	73, 65, 60	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
52	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.neg_int_within_rational_neg
53	instantiation	61, 62	⊢
	:
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
55	instantiation	73, 63, 64	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	instantiation	73, 65, 66	⊢
	: , : , :
58	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
60	instantiation	73, 70, 67	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.negation.int_neg_closure
62	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
64	instantiation	73, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
66	instantiation	73, 70, 71	⊢
	: , : , :
67	instantiation	73, 74, 72	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
70	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
71	instantiation	73, 74, 75	⊢
	: , : , :
72	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
73	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
74	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
75	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements