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^*	⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.weak_bound_via_right_term_bound
2	reference	48	⊢
3	instantiation	7, 68, 48, 8	⊢
	: , :
4	instantiation	75, 9, 10	⊢
	: , : , :
5	instantiation	11, 12, 47, 53, 13	⊢
	: , : , :
6	instantiation	14, 62, 74, 15^, 16^, 17^*	⊢
	: , : , : , :
7	theorem		⊢
	proveit.numbers.division.div_real_closure
8	instantiation	18, 64	⊢
	:
9	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
10	instantiation	19, 20, 47, 21	⊢
	: , :
11	theorem		⊢
	proveit.numbers.division.weak_div_from_denom_bound__all_pos
12	instantiation	75, 22, 23	⊢
	: , : , :
13	instantiation	24, 48, 60, 68, 25, 26, 27^*	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
15	instantiation	28, 39	⊢
	:
16	instantiation	29, 30, 31	⊢
	: , : , :
17	instantiation	32, 39	⊢
	:
18	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
19	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
20	instantiation	75, 57, 33	⊢
	: , : , :
21	instantiation	34, 35	⊢
	:
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_nonneg_within_real_nonneg
23	instantiation	75, 36, 77	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.multiplication.weak_bound_via_right_factor_bound
25	instantiation	37, 67, 68, 69	⊢
	: , : , :
26	instantiation	38, 70	⊢
	:
27	instantiation	50, 39	⊢
	:
28	theorem		⊢
	proveit.numbers.division.frac_one_denom
29	axiom		⊢
	proveit.logic.equality.equals_transitivity
30	instantiation	40, 70, 41, 42, 43, 44	⊢
	: , : , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.add_4_1
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
33	instantiation	75, 63, 45	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nonzero_if_in_real_nonzero
35	instantiation	75, 46, 47	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_within_rational_nonneg
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_upper_bound
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
39	instantiation	75, 56, 48	⊢
	: , : , :
40	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
41	instantiation	49	⊢
	: , :
42	instantiation	49	⊢
	: , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
44	instantiation	50, 51	⊢
	:
45	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
46	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real_nonzero
47	instantiation	52, 53, 54	⊢
	: , :
48	instantiation	75, 71, 55	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
51	instantiation	75, 56, 68	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
53	instantiation	75, 57, 58	⊢
	: , : , :
54	instantiation	59, 60, 61	⊢
	:
55	instantiation	75, 73, 62	⊢
	: , : , :
56	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
57	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
58	instantiation	75, 63, 64	⊢
	: , : , :
59	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
60	instantiation	65, 67, 68, 69	⊢
	: , : , :
61	instantiation	66, 67, 68, 69	⊢
	: , : , :
62	instantiation	75, 76, 70	⊢
	: , : , :
63	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
64	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
65	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
66	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
67	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
68	instantiation	75, 71, 72	⊢
	: , : , :
69	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
70	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
71	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
72	instantiation	75, 73, 74	⊢
	: , : , :
73	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
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.nat1
^*equality replacement requirements