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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 9, 8, 11, 10, 13, 14, 15, 12	⊢
	: , : , : , : , : , : , :
5	instantiation	7, 62, 8, 9, 10, 11, 12, 13, 14, 15	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	theorem		⊢
	proveit.numbers.multiplication.association
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	16	⊢
	: , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
13	instantiation	63, 19, 17	⊢
	: , : , :
14	instantiation	63, 19, 18	⊢
	: , : , :
15	instantiation	63, 19, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
17	instantiation	63, 37, 21	⊢
	: , : , :
18	instantiation	63, 22, 23	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
20	instantiation	24, 25, 26	⊢
	: , :
21	instantiation	63, 39, 27	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
24	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
25	instantiation	28, 29	⊢
	:
26	instantiation	30, 31	⊢
	:
27	instantiation	63, 61, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
29	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
30	theorem		⊢
	proveit.numbers.negation.real_closure
31	instantiation	33, 34, 35	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
34	instantiation	63, 37, 36	⊢
	: , : , :
35	instantiation	63, 37, 38	⊢
	: , : , :
36	instantiation	63, 39, 40	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	63, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	63, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
42	instantiation	45, 46, 47	⊢
	: , :
43	instantiation	48, 49, 60	⊢
	: , :
44	assumption		⊢
45	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
46	instantiation	63, 50, 51	⊢
	: , : , :
47	instantiation	59, 52	⊢
	:
48	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
49	instantiation	53, 54, 55	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
51	instantiation	63, 56, 57	⊢
	: , : , :
52	instantiation	63, 64, 58	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
54	instantiation	59, 60	⊢
	:
55	instantiation	63, 61, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
58	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
59	theorem		⊢
	proveit.numbers.negation.int_closure
60	instantiation	63, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
62	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
63	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
65	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos