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	theorem		⊢
	proveit.logic.equality.equals_reversal
2	instantiation	3, 4	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.substitution
4	instantiation	5, 6, 7	⊢
	: , : , :
5	axiom		⊢
	proveit.logic.equality.equals_transitivity
6	instantiation	8, 12, 38, 54, 14, 9, 16, 17, 15, 18	⊢
	: , : , : , : , : , : , :
7	instantiation	10, 54, 11, 12, 13, 14, 15, 16, 17, 18	⊢
	: , : , : , : , : , :
8	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
9	instantiation	19	⊢
	: , :
10	theorem		⊢
	proveit.numbers.multiplication.association
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	instantiation	20	⊢
	: , : , :
14	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
15	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
16	instantiation	55, 23, 21	⊢
	: , : , :
17	instantiation	55, 23, 22	⊢
	: , : , :
18	instantiation	55, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
21	instantiation	55, 40, 25	⊢
	: , : , :
22	instantiation	55, 26, 27	⊢
	: , : , :
23	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
24	instantiation	28, 29, 30	⊢
	: , :
25	instantiation	55, 42, 31	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
28	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
29	instantiation	32, 33, 34, 35	⊢
	: , : , :
30	instantiation	36, 37	⊢
	:
31	instantiation	55, 53, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
34	instantiation	55, 40, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.physics.quantum.QPE._scaled_delta_b_floor_in_interval
36	theorem		⊢
	proveit.numbers.negation.real_closure
37	instantiation	55, 40, 41	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
39	instantiation	55, 42, 50	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	55, 42, 43	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
43	instantiation	55, 44, 45	⊢
	: , : , :
44	instantiation	46, 47, 52	⊢
	: , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
47	instantiation	48, 49, 50	⊢
	: , :
48	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
49	instantiation	51, 52	⊢
	:
50	instantiation	55, 53, 54	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.negation.int_closure
52	instantiation	55, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
54	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
57	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos