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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 4	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.substitution
4	instantiation	5, 6, 7	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	8, 12, 36, 66, 14, 9, 16, 17, 15, 18	⊢
	: , : , : , : , : , : , :
7	instantiation	10, 66, 11, 12, 13, 14, 15, 16, 17, 18	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
9	instantiation	19	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.association
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	instantiation	20	⊢
	: , : , :
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
16	instantiation	67, 23, 21	⊢
	: , : , :
17	instantiation	67, 23, 22	⊢
	: , : , :
18	instantiation	67, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
21	instantiation	67, 41, 25	⊢
	: , : , :
22	instantiation	67, 26, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	28, 29, 30	⊢
	: , :
25	instantiation	67, 43, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	instantiation	32, 33	⊢
	:
30	instantiation	34, 35	⊢
	:
31	instantiation	67, 65, 36	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.negation.real_closure
33	instantiation	37, 38, 39	⊢
	: , :
34	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
35	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
38	instantiation	67, 41, 40	⊢
	: , : , :
39	instantiation	67, 41, 42	⊢
	: , : , :
40	instantiation	67, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
42	instantiation	67, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	67, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
46	instantiation	49, 50, 51	⊢
	: , :
47	instantiation	52, 53, 64	⊢
	: , :
48	assumption		⊢
49	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
50	instantiation	67, 54, 55	⊢
	: , : , :
51	instantiation	63, 56	⊢
	:
52	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
53	instantiation	57, 58, 59	⊢
	: , :
54	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
55	instantiation	67, 60, 61	⊢
	: , : , :
56	instantiation	67, 68, 62	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
58	instantiation	63, 64	⊢
	:
59	instantiation	67, 65, 66	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
62	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
63	theorem		⊢
	proveit.numbers.negation.int_closure
64	instantiation	67, 68, 69	⊢
	: , : , :
65	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
66	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
67	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
68	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
69	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos