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	reference	27	⊢
2	instantiation	4, 53, 6, 8, 35, 11, 10	⊢
	: , : , : , : , : , : , :
3	instantiation	5, 6, 7, 53, 8, 9, 35, 10, 11, 12^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.multiplication.association
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	13	⊢
	: , :
10	instantiation	14, 35, 15	⊢
	: , :
11	instantiation	51, 42, 16	⊢
	: , : , :
12	instantiation	17, 35, 43, 21, 18, 19^, 20^	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
15	instantiation	51, 42, 21	⊢
	: , : , :
16	instantiation	22, 23	⊢
	:
17	theorem		⊢
	proveit.numbers.exponentiation.product_of_real_powers
18	instantiation	24, 25	⊢
	:
19	instantiation	26, 35	⊢
	:
20	instantiation	27, 28, 29	⊢
	: , : , :
21	instantiation	51, 47, 30	⊢
	: , : , :
22	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
23	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
25	instantiation	51, 31, 46	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.complex_x_to_first_power_is_x
27	axiom		⊢
	proveit.logic.equality.equals_transitivity
28	instantiation	32, 33	⊢
	: , : , :
29	instantiation	34, 35	⊢
	:
30	instantiation	51, 49, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
32	axiom		⊢
	proveit.logic.equality.substitution
33	instantiation	37, 38, 39	⊢
	: , :
34	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
35	instantiation	51, 42, 40	⊢
	: , : , :
36	instantiation	41, 50	⊢
	:
37	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
38	instantiation	51, 42, 43	⊢
	: , : , :
39	instantiation	44	⊢
	:
40	instantiation	51, 45, 46	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.negation.int_closure
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	51, 47, 48	⊢
	: , : , :
44	axiom		⊢
	proveit.logic.equality.equals_reflexivity
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	51, 49, 50	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
50	instantiation	51, 52, 53	⊢
	: , : , :
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
53	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements