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	, ⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.equals_transitivity
2	instantiation	4, 9, 34, 11, 5, 6, 20, 13, 12, 14, 15	, ⊢
	: , : , : , : , : , : , :
3	instantiation	7, 48, 8, 9, 10, 11, 12, 20, 13, 14, 15	, ⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	instantiation	16	⊢
	: , :
6	instantiation	16	⊢
	: , :
7	theorem		⊢
	proveit.numbers.multiplication.association
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	17	⊢
	: , : , : , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
13	instantiation	49, 29, 18	⊢
	: , : , :
14	instantiation	19, 20, 21	, ⊢
	: , :
15	instantiation	49, 29, 22	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
18	instantiation	49, 23, 24	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
20	instantiation	49, 29, 25	⊢
	: , : , :
21	instantiation	26, 27	, ⊢
	:
22	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
25	instantiation	49, 32, 28	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.negation.complex_closure
27	instantiation	49, 29, 30	, ⊢
	: , : , :
28	instantiation	49, 35, 31	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	49, 32, 33	, ⊢
	: , : , :
31	instantiation	49, 47, 34	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	49, 35, 36	, ⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
35	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
36	instantiation	49, 37, 38	, ⊢
	: , : , :
37	instantiation	39, 40, 41	⊢
	: , :
38	assumption		⊢
39	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
40	instantiation	42, 43, 44	⊢
	: , :
41	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
42	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
43	instantiation	45, 46	⊢
	:
44	instantiation	49, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.negation.int_closure
46	instantiation	49, 50, 51	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
48	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
51	assumption		⊢