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