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, 4, 5, 6, 7, 8, 9^*	⊢
	: , : , : , : , : , :
1	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
2	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
3	reference	77	⊢
4	reference	67	⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
6	instantiation	10	⊢
	: , :
7	instantiation	75, 13, 20	⊢
	: , : , :
8	reference	12	⊢
9	instantiation	11, 12	⊢
	:
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
11	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
12	instantiation	75, 13, 14	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
14	modus ponens	15, 16	⊢
15	instantiation	17	⊢
	: , : , :
16	generalization	18	⊢
17	theorem		⊢
	proveit.numbers.summation.summation_real_closure
18	instantiation	19, 20, 21, 22	, ⊢
	: , :
19	theorem		⊢
	proveit.numbers.division.div_real_closure
20	instantiation	75, 29, 23	⊢
	: , : , :
21	instantiation	24, 25, 77	, ⊢
	: , :
22	instantiation	26, 27, 28	, ⊢
	: , :
23	instantiation	75, 34, 64	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
25	instantiation	75, 29, 30	, ⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_non_zero__not_zero
27	instantiation	75, 32, 31	, ⊢
	: , : , :
28	instantiation	75, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
30	instantiation	75, 34, 38	, ⊢
	: , : , :
31	instantiation	75, 36, 35	, ⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
33	instantiation	75, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
35	instantiation	51, 38, 39	, ⊢
	:
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
38	instantiation	75, 40, 47	, ⊢
	: , : , :
39	instantiation	57, 41, 42	, ⊢
	: , : , :
40	instantiation	62, 45, 46	⊢
	: , :
41	instantiation	43, 44	⊢
	:
42	instantiation	63, 45, 46, 47	, ⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
44	instantiation	48, 49, 61	⊢
	: , :
45	instantiation	68, 52, 64	⊢
	: , :
46	instantiation	68, 69, 50	⊢
	: , :
47	assumption		⊢
48	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
49	instantiation	51, 52, 53	⊢
	:
50	instantiation	75, 54, 55	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
52	instantiation	75, 56, 66	⊢
	: , : , :
53	instantiation	57, 58, 59	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
55	instantiation	60, 61	⊢
	:
56	instantiation	62, 64, 65	⊢
	: , :
57	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
58	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
59	instantiation	63, 64, 65, 66	⊢
	: , : , :
60	theorem		⊢
	proveit.numbers.negation.int_neg_closure
61	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
62	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
63	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
64	instantiation	75, 76, 67	⊢
	: , : , :
65	instantiation	68, 69, 70	⊢
	: , :
66	assumption		⊢
67	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
68	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
69	instantiation	75, 71, 72	⊢
	: , : , :
70	instantiation	73, 74	⊢
	:
71	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
72	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
73	theorem		⊢
	proveit.numbers.negation.int_closure
74	instantiation	75, 76, 77	⊢
	: , : , :
75	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
76	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
77	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements