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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 7, 6, 9, 8, 11, 12, 13, 10	⊢
	: , : , : , : , : , : , :
3	instantiation	5, 60, 6, 7, 8, 9, 10, 11, 12, 13	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.multiplication.association
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	instantiation	14	⊢
	: , : , :
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
11	instantiation	61, 17, 15	⊢
	: , : , :
12	instantiation	61, 17, 16	⊢
	: , : , :
13	instantiation	61, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
15	instantiation	61, 35, 19	⊢
	: , : , :
16	instantiation	61, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
18	instantiation	22, 23, 24	⊢
	: , :
19	instantiation	61, 37, 25	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
22	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
23	instantiation	26, 27	⊢
	:
24	instantiation	28, 29	⊢
	:
25	instantiation	61, 59, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
27	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	31, 32, 33	⊢
	: , :
30	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
31	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
32	instantiation	61, 35, 34	⊢
	: , : , :
33	instantiation	61, 35, 36	⊢
	: , : , :
34	instantiation	61, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
36	instantiation	61, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	61, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
40	instantiation	43, 44, 45	⊢
	: , :
41	instantiation	46, 47, 58	⊢
	: , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
44	instantiation	61, 48, 49	⊢
	: , : , :
45	instantiation	57, 50	⊢
	:
46	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
47	instantiation	51, 52, 53	⊢
	: , :
48	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
49	instantiation	61, 54, 55	⊢
	: , : , :
50	instantiation	61, 62, 56	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
52	instantiation	57, 58	⊢
	:
53	instantiation	61, 59, 60	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
56	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
57	theorem		⊢
	proveit.numbers.negation.int_closure
58	instantiation	61, 62, 63	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
61	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
63	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos