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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 11, 9, 39, 13, 7, 15, 14, 16, 17	⊢
	: , : , : , : , : , : , :
5	instantiation	8, 9, 10, 11, 12, 13, 14, 15, 16, 17	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	instantiation	18	⊢
	: , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	19	⊢
	: , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	43, 44, 20	⊢
	: , : , :
15	instantiation	43, 44, 21	⊢
	: , : , :
16	instantiation	43, 44, 22	⊢
	: , : , :
17	instantiation	43, 44, 23	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
20	instantiation	43, 24, 25	⊢
	: , : , :
21	instantiation	26, 27, 28	⊢
	: , : , :
22	instantiation	43, 30, 29	⊢
	: , : , :
23	instantiation	43, 30, 31	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
25	instantiation	43, 32, 33	⊢
	: , : , :
26	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
27	instantiation	34, 35	⊢
	: , :
28	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
31	instantiation	36, 37	⊢
	:
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
33	instantiation	43, 38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
36	theorem		⊢
	proveit.numbers.absolute_value.abs_nonzero_closure
37	instantiation	40, 41, 42	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
41	instantiation	43, 44, 45	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	46, 47	⊢
	:
46	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_is_real
47	theorem		⊢
	proveit.physics.quantum.QPE._best_round_is_int