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