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