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, 10, 11	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.disassociation
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
4	reference	55	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	12	⊢
	: , : , : , :
7	instantiation	56, 33, 13	⊢
	: , : , :
8	instantiation	56, 33, 14	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
10	instantiation	15, 16, 17	⊢
	: , :
11	reference	29	⊢
12	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
13	instantiation	56, 36, 18	⊢
	: , : , :
14	instantiation	56, 19, 20	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
16	instantiation	56, 33, 21	⊢
	: , : , :
17	instantiation	22, 23	⊢
	:
18	instantiation	56, 41, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
21	instantiation	25, 26	⊢
	:
22	theorem		⊢
	proveit.numbers.negation.complex_closure
23	instantiation	27, 28, 29, 30	⊢
	: , :
24	instantiation	56, 54, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
26	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
27	theorem		⊢
	proveit.numbers.division.div_complex_closure
28	instantiation	56, 33, 32	⊢
	: , : , :
29	instantiation	56, 33, 34	⊢
	: , : , :
30	instantiation	35, 40	⊢
	:
31	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
32	instantiation	56, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	38, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	56, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
39	instantiation	43, 44	⊢
	: , :
40	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	56, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
45	instantiation	47, 48, 53	⊢
	: , :
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
48	instantiation	49, 50, 51	⊢
	: , :
49	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
50	instantiation	52, 53	⊢
	:
51	instantiation	56, 54, 55	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.negation.int_closure
53	instantiation	56, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
56	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
58	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos