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	reference	62	⊢
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
3	instantiation	62, 4, 5	, ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
5	instantiation	6, 7, 64	, ⊢
	: , :
6	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
7	instantiation	8, 9, 10	, ⊢
	:
8	theorem		⊢
	proveit.numbers.number_sets.integers.nonneg_int_is_natural
9	instantiation	52, 11, 12	, ⊢
	: , :
10	instantiation	13, 14	, ⊢
	: , :
11	instantiation	62, 15, 30	, ⊢
	: , : , :
12	instantiation	62, 16, 17	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.ordering.relax_less
14	instantiation	18, 19	, ⊢
	: , :
15	instantiation	48, 29, 53	⊢
	: , :
16	theorem		⊢
	proveit.numbers.number_sets.integers.neg_int_within_int
17	instantiation	20, 21	⊢
	:
18	theorem		⊢
	proveit.numbers.addition.subtraction.pos_difference
19	instantiation	32, 22, 23	, ⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.negation.int_neg_closure
21	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
22	instantiation	24, 47, 25, 26, 27, 28^*	⊢
	: , : , :
23	instantiation	39, 29, 53, 30	, ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
25	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
26	instantiation	62, 50, 31	⊢
	: , : , :
27	instantiation	32, 33, 34	⊢
	: , : , :
28	instantiation	35, 36, 37	⊢
	: , : , :
29	instantiation	52, 38, 56	⊢
	: , :
30	assumption		⊢
31	instantiation	62, 55, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
33	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
34	instantiation	39, 56, 49, 45	⊢
	: , : , :
35	theorem		⊢
	proveit.logic.equality.sub_right_side_into
36	instantiation	40, 42	⊢
	:
37	instantiation	41, 42, 43	⊢
	: , :
38	instantiation	62, 44, 45	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
40	theorem		⊢
	proveit.numbers.addition.elim_zero_right
41	theorem		⊢
	proveit.numbers.addition.commutation
42	instantiation	62, 46, 47	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
44	instantiation	48, 56, 49	⊢
	: , :
45	assumption		⊢
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	62, 50, 51	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
49	instantiation	52, 53, 54	⊢
	: , :
50	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
51	instantiation	62, 55, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
53	instantiation	62, 57, 58	⊢
	: , : , :
54	instantiation	59, 60	⊢
	:
55	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
56	instantiation	62, 63, 61	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
58	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
59	theorem		⊢
	proveit.numbers.negation.int_closure
60	instantiation	62, 63, 64	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
62	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
63	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
64	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements