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	5, 49, 7, 6, 10, 8, 4, 11, 12, 13	, ⊢
	: , : , : , : , : , :
3	instantiation	5, 6, 44, 7, 8, 9, 10, 15, 16, 11, 12, 13	, ⊢
	: , : , : , : , : , :
4	instantiation	14, 15, 16	⊢
	: , :
5	theorem		⊢
	proveit.numbers.multiplication.disassociation
6	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
7	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
8	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
9	instantiation	17	⊢
	: , :
10	instantiation	18	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
12	instantiation	47, 22, 19	⊢
	: , : , :
13	instantiation	47, 22, 20	, ⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
15	instantiation	47, 22, 21	⊢
	: , : , :
16	instantiation	47, 22, 23	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
20	instantiation	47, 25, 24	, ⊢
	: , : , :
21	instantiation	47, 25, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	instantiation	47, 27, 28	⊢
	: , : , :
24	instantiation	47, 30, 29	, ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
26	instantiation	47, 30, 40	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
29	instantiation	47, 31, 32	, ⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
31	instantiation	33, 34, 35	⊢
	: , :
32	assumption		⊢
33	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
34	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
35	instantiation	36, 37, 38	⊢
	: , :
36	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
37	instantiation	39, 40, 41	⊢
	: , :
38	instantiation	42, 43	⊢
	:
39	theorem		⊢
	proveit.numbers.exponentiation.exp_int_closure
40	instantiation	47, 48, 44	⊢
	: , : , :
41	instantiation	47, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.negation.int_closure
43	instantiation	47, 48, 49	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
45	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
46	assumption		⊢
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat1