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, 4, 5, 6, 7, 8, 9	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.addition.disassociation
2	reference	68	⊢
3	reference	63	⊢
4	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
5	instantiation	10	⊢
	: , :
6	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
7	instantiation	66, 12, 15	⊢
	: , : , :
8	instantiation	66, 12, 11	⊢
	: , : , :
9	instantiation	66, 12, 13	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	instantiation	17, 14, 47, 19	⊢
	: , :
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
13	instantiation	27, 15	⊢
	:
14	instantiation	20, 21, 16	⊢
	: , :
15	instantiation	17, 18, 47, 19	⊢
	: , :
16	instantiation	27, 43	⊢
	:
17	theorem		⊢
	proveit.numbers.modular.mod_abs_real_closure
18	instantiation	20, 21, 22	⊢
	: , :
19	instantiation	23, 24, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
21	instantiation	66, 56, 26	⊢
	: , : , :
22	instantiation	27, 28	⊢
	:
23	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
24	instantiation	66, 30, 29	⊢
	: , : , :
25	instantiation	66, 30, 31	⊢
	: , : , :
26	instantiation	66, 61, 32	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.negation.real_closure
28	instantiation	66, 56, 33	⊢
	: , : , :
29	instantiation	66, 35, 34	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
31	instantiation	66, 35, 65	⊢
	: , : , :
32	instantiation	66, 36, 37	⊢
	: , : , :
33	instantiation	66, 61, 38	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
35	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
36	instantiation	39, 40, 41	⊢
	: , :
37	assumption		⊢
38	instantiation	42, 43	⊢
	:
39	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
40	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
41	instantiation	44, 55, 45	⊢
	: , :
42	axiom		⊢
	proveit.numbers.rounding.floor_is_an_int
43	instantiation	46, 47, 48	⊢
	: , :
44	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
45	instantiation	49, 62	⊢
	:
46	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
47	instantiation	66, 56, 50	⊢
	: , : , :
48	instantiation	51, 52, 53, 54	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.negation.int_closure
50	instantiation	66, 61, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
53	instantiation	66, 56, 57	⊢
	: , : , :
54	axiom		⊢
	proveit.physics.quantum.QPE._phase_in_interval
55	instantiation	58, 59, 60	⊢
	: , :
56	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
57	instantiation	66, 61, 62	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
59	instantiation	66, 67, 63	⊢
	: , : , :
60	instantiation	66, 64, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
62	instantiation	66, 67, 68	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
64	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
65	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
66	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
67	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1