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	reference	5	⊢
2	instantiation	28, 3, 4	⊢
	: , : , :
3	instantiation	5, 6	⊢
	: , : , :
4	instantiation	7, 8	⊢
	: , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	instantiation	9, 36, 10, 68, 37, 11, 45, 46, 40, 41, 12	⊢
	: , : , : , : , : , :
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	13, 14, 15, 16	⊢
	: , :
9	theorem		⊢
	proveit.numbers.multiplication.association
10	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
11	instantiation	17	⊢
	: , : , : , :
12	instantiation	69, 53, 18	⊢
	: , : , :
13	instantiation	19, 33	⊢
	:
14	instantiation	69, 53, 20	⊢
	: , : , :
15	instantiation	21, 22, 23	⊢
	: , : , :
16	instantiation	24, 25	⊢
	:
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_4_typical_eq
18	instantiation	69, 58, 26	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.int_exp_of_exp
20	instantiation	69, 60, 32	⊢
	: , : , :
21	theorem		⊢
	proveit.logic.equality.sub_right_side_into
22	instantiation	44, 34, 27	⊢
	: , :
23	instantiation	28, 29, 30	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
25	instantiation	69, 31, 32	⊢
	: , : , :
26	instantiation	69, 66, 33	⊢
	: , : , :
27	instantiation	44, 40, 41	⊢
	: , :
28	axiom		⊢
	proveit.logic.equality.equals_transitivity
29	instantiation	35, 68, 71, 36, 39, 37, 34, 40, 41	⊢
	: , : , : , : , : , :
30	instantiation	35, 36, 71, 37, 38, 39, 45, 46, 40, 41	⊢
	: , : , : , : , : , :
31	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
33	instantiation	69, 42, 43	⊢
	: , : , :
34	instantiation	44, 45, 46	⊢
	: , :
35	theorem		⊢
	proveit.numbers.multiplication.disassociation
36	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	instantiation	47	⊢
	: , :
39	instantiation	47	⊢
	: , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
41	instantiation	69, 53, 48	⊢
	: , : , :
42	instantiation	49, 50, 51	⊢
	: , :
43	assumption		⊢
44	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
45	instantiation	69, 53, 52	⊢
	: , : , :
46	instantiation	69, 53, 54	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
48	theorem		⊢
	proveit.physics.quantum.QPE._phase_is_real
49	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
50	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
51	instantiation	55, 56, 57	⊢
	: , :
52	instantiation	69, 58, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
54	instantiation	69, 60, 61	⊢
	: , : , :
55	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
56	instantiation	69, 62, 63	⊢
	: , : , :
57	instantiation	64, 65	⊢
	:
58	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
59	instantiation	69, 66, 67	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
61	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
62	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
63	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
64	theorem		⊢
	proveit.numbers.negation.int_closure
65	instantiation	69, 70, 68	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
67	instantiation	69, 70, 71	⊢
	: , : , :
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
69	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
70	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
71	theorem		⊢
	proveit.numbers.numerals.decimals.nat2