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	⊢
	: , : , :
1	reference	25	⊢
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	25, 6	⊢
	: , : , :
5	instantiation	7, 73, 70, 8, 9, 10, 42, 11, 12	⊢
	: , : , : , : , : , :
6	instantiation	13, 14, 15, 16	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.multiplication.disassociation
8	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
9	instantiation	17	⊢
	: , :
10	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
11	instantiation	18, 28, 19, 20	⊢
	: , :
12	instantiation	71, 49, 21	⊢
	: , : , :
13	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
14	instantiation	25, 22	⊢
	: , : , :
15	instantiation	23, 24	⊢
	: , :
16	instantiation	25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	theorem		⊢
	proveit.numbers.division.div_complex_closure
19	instantiation	27, 42, 28	⊢
	: , :
20	instantiation	29, 36, 30	⊢
	: , : , :
21	instantiation	51, 52, 31	⊢
	: , : , :
22	instantiation	32, 33, 34	⊢
	: , :
23	theorem		⊢
	proveit.logic.equality.equals_reversal
24	instantiation	35, 42, 44, 43, 36	⊢
	: , : , :
25	axiom		⊢
	proveit.logic.equality.substitution
26	instantiation	37, 38, 39	⊢
	: , :
27	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
28	instantiation	71, 49, 40	⊢
	: , : , :
29	theorem		⊢
	proveit.logic.equality.sub_left_side_into
30	instantiation	41, 42	⊢
	:
31	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
32	theorem		⊢
	proveit.numbers.addition.commutation
33	instantiation	71, 49, 43	⊢
	: , : , :
34	instantiation	71, 49, 44	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
36	instantiation	45, 69	⊢
	:
37	theorem		⊢
	proveit.numbers.exponentiation.neg_power_as_div
38	instantiation	71, 46, 47	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
40	instantiation	71, 57, 48	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
42	instantiation	71, 49, 50	⊢
	: , : , :
43	instantiation	51, 52, 53	⊢
	: , : , :
44	instantiation	71, 57, 54	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_nonzero_within_complex_nonzero
47	instantiation	71, 55, 56	⊢
	: , : , :
48	instantiation	71, 64, 67	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
50	instantiation	71, 57, 58	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
52	instantiation	59, 60	⊢
	: , :
53	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
54	instantiation	71, 64, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonzero_within_real_nonzero
56	instantiation	71, 62, 63	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
58	instantiation	71, 64, 65	⊢
	: , : , :
59	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
61	instantiation	66, 67	⊢
	:
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
63	instantiation	71, 68, 69	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
65	instantiation	71, 72, 70	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.negation.int_closure
67	instantiation	71, 72, 73	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
72	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
73	theorem		⊢
	proveit.numbers.numerals.decimals.nat1