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	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 9, 37, 7, 11, 5, 13, 14, 12, 15	⊢
	: , : , : , : , : , : , :
3	instantiation	6, 7, 8, 9, 10, 11, 12, 13, 14, 15	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	instantiation	16	⊢
	: , :
6	theorem		⊢
	proveit.numbers.multiplication.association
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	17	⊢
	: , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	41, 42, 18	⊢
	: , : , :
13	instantiation	41, 42, 19	⊢
	: , : , :
14	instantiation	41, 42, 20	⊢
	: , : , :
15	instantiation	41, 42, 21	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
18	instantiation	41, 28, 22	⊢
	: , : , :
19	instantiation	41, 23, 24	⊢
	: , : , :
20	instantiation	25, 26, 27	⊢
	: , : , :
21	instantiation	41, 28, 29	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
24	instantiation	41, 30, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
26	instantiation	32, 33	⊢
	: , :
27	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
29	instantiation	34, 35	⊢
	:
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	41, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
34	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
35	instantiation	38, 39, 40	⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
39	instantiation	41, 42, 43	⊢
	: , : , :
40	assumption		⊢
41	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
42	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
43	instantiation	44, 45	⊢
	:
44	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
45	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int