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, 9	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.disassociation
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	69	⊢
4	reference	61	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	10	⊢
	: , :
7	reference	19	⊢
8	instantiation	67, 47, 11	⊢
	: , : , :
9	instantiation	12, 13, 14, 15, 32, 16	⊢
	: , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	instantiation	67, 54, 17	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.addition.add_complex_closure
13	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
14	instantiation	18	⊢
	: , : , :
15	instantiation	20, 19	⊢
	:
16	instantiation	20, 21	⊢
	:
17	instantiation	67, 62, 60	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	instantiation	22, 23, 24	⊢
	: , :
20	theorem		⊢
	proveit.numbers.negation.complex_closure
21	instantiation	67, 47, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
23	instantiation	26, 32, 27, 28	⊢
	: , :
24	instantiation	67, 47, 29	⊢
	: , : , :
25	instantiation	67, 54, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.division.div_complex_closure
27	instantiation	31, 42, 32	⊢
	: , :
28	instantiation	33, 34, 35	⊢
	: , : , :
29	instantiation	67, 54, 36	⊢
	: , : , :
30	instantiation	67, 62, 37	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
32	instantiation	67, 47, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.logic.equality.sub_left_side_into
34	instantiation	39, 40	⊢
	:
35	instantiation	41, 42	⊢
	:
36	instantiation	67, 62, 43	⊢
	: , : , :
37	instantiation	67, 44, 45	⊢
	: , : , :
38	instantiation	67, 54, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
42	instantiation	67, 47, 48	⊢
	: , : , :
43	instantiation	49, 66, 50	⊢
	: , :
44	instantiation	51, 53, 52	⊢
	: , :
45	assumption		⊢
46	instantiation	67, 62, 53	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
48	instantiation	67, 54, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
50	instantiation	67, 56, 57	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
52	instantiation	58, 59, 60	⊢
	: , :
53	instantiation	67, 68, 61	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
55	instantiation	67, 62, 66	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
57	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
58	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
59	instantiation	67, 63, 64	⊢
	: , : , :
60	instantiation	65, 66	⊢
	:
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
62	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
64	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
65	theorem		⊢
	proveit.numbers.negation.int_closure
66	instantiation	67, 68, 69	⊢
	: , : , :
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
69	theorem		⊢
	proveit.numbers.numerals.decimals.nat2