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	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
2	instantiation	68, 5, 4	⊢
	: , : , :
3	instantiation	68, 5, 6	⊢
	: , : , :
4	instantiation	68, 22, 7	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
6	modus ponens	8, 9	⊢
7	instantiation	68, 27, 67	⊢
	: , : , :
8	instantiation	10	⊢
	: , : , :
9	generalization	11	⊢
10	theorem		⊢
	proveit.numbers.summation.summation_real_closure
11	instantiation	12, 13, 14, 15	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.division.div_real_closure
13	instantiation	68, 22, 16	⊢
	: , : , :
14	instantiation	17, 18, 70	, ⊢
	: , :
15	instantiation	19, 20, 21	, ⊢
	: , :
16	instantiation	68, 27, 57	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
18	instantiation	68, 22, 23	, ⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
20	instantiation	68, 25, 24	, ⊢
	: , : , :
21	instantiation	68, 25, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
23	instantiation	68, 27, 31	, ⊢
	: , : , :
24	instantiation	68, 29, 28	, ⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
26	instantiation	68, 29, 30	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
28	instantiation	44, 31, 32	, ⊢
	:
29	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
31	instantiation	68, 33, 40	, ⊢
	: , : , :
32	instantiation	50, 34, 35	, ⊢
	: , : , :
33	instantiation	55, 38, 39	⊢
	: , :
34	instantiation	36, 37	⊢
	:
35	instantiation	56, 38, 39, 40	, ⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
37	instantiation	41, 42, 54	⊢
	: , :
38	instantiation	61, 45, 57	⊢
	: , :
39	instantiation	61, 62, 43	⊢
	: , :
40	assumption		⊢
41	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
42	instantiation	44, 45, 46	⊢
	:
43	instantiation	68, 47, 48	⊢
	: , : , :
44	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
45	instantiation	68, 49, 59	⊢
	: , : , :
46	instantiation	50, 51, 52	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
48	instantiation	53, 54	⊢
	:
49	instantiation	55, 57, 58	⊢
	: , :
50	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
51	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
52	instantiation	56, 57, 58, 59	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.negation.int_neg_closure
54	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
55	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
56	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
57	instantiation	68, 69, 60	⊢
	: , : , :
58	instantiation	61, 62, 63	⊢
	: , :
59	assumption		⊢
60	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
61	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
62	instantiation	68, 64, 65	⊢
	: , : , :
63	instantiation	66, 67	⊢
	:
64	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
65	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
66	theorem		⊢
	proveit.numbers.negation.int_closure
67	instantiation	68, 69, 70	⊢
	: , : , :
68	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
69	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2