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	⊢
	: , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
4	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
5	instantiation	9	⊢
	: , : , :
6	reference	12	⊢
7	instantiation	58, 18, 10	⊢
	: , : , :
8	instantiation	11, 12, 13	⊢
	: , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
10	instantiation	14, 15, 16	⊢
	: , :
11	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
12	instantiation	58, 18, 17	⊢
	: , : , :
13	instantiation	58, 18, 19	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
15	instantiation	20, 21	⊢
	:
16	instantiation	22, 23	⊢
	:
17	instantiation	58, 24, 25	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
19	instantiation	58, 32, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
21	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
22	theorem		⊢
	proveit.numbers.negation.real_closure
23	instantiation	27, 28, 29	⊢
	: , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
26	instantiation	58, 34, 30	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
28	instantiation	58, 32, 31	⊢
	: , : , :
29	instantiation	58, 32, 33	⊢
	: , : , :
30	instantiation	54, 50	⊢
	:
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