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, 11, 36, 13, 7, 8, 22, 15, 14, 16, 17	, ⊢
	: , : , : , : , : , : , :
5	instantiation	9, 50, 10, 11, 12, 13, 14, 22, 15, 16, 17	, ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	instantiation	18	⊢
	: , :
8	instantiation	18	⊢
	: , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
12	instantiation	19	⊢
	: , : , : , :
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
15	instantiation	51, 31, 20	⊢
	: , : , :
16	instantiation	21, 22, 23	, ⊢
	: , :
17	instantiation	51, 31, 24	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
20	instantiation	51, 25, 26	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
22	instantiation	51, 31, 27	⊢
	: , : , :
23	instantiation	28, 29	, ⊢
	:
24	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
27	instantiation	51, 34, 30	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.negation.complex_closure
29	instantiation	51, 31, 32	, ⊢
	: , : , :
30	instantiation	51, 37, 33	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
32	instantiation	51, 34, 35	, ⊢
	: , : , :
33	instantiation	51, 49, 36	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	51, 37, 38	, ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
38	instantiation	51, 39, 40	, ⊢
	: , : , :
39	instantiation	41, 42, 43	⊢
	: , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
42	instantiation	44, 45, 46	⊢
	: , :
43	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
44	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
45	instantiation	47, 48	⊢
	:
46	instantiation	51, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.negation.int_closure
48	instantiation	51, 52, 53	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
51	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
52	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
53	assumption		⊢