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	theorem		⊢
	proveit.numbers.ordering.relax_less
2	instantiation	27, 3, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 45, 8, 9	⊢
	: , : , :
4	instantiation	10, 11, 12	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
6	instantiation	62, 52, 13	⊢
	: , : , :
7	instantiation	62, 52, 14	⊢
	: , : , :
8	instantiation	15, 56, 41, 31	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	16, 19, 64, 59, 21, 17, 22, 39, 38	⊢
	: , : , : , : , : , :
12	instantiation	18, 59, 64, 19, 20, 21, 22, 39, 38, 23^*	⊢
	: , : , : , : , : , :
13	instantiation	62, 57, 24	⊢
	: , : , :
14	instantiation	62, 57, 41	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
16	theorem		⊢
	proveit.numbers.addition.disassociation
17	instantiation	25	⊢
	: , :
18	theorem		⊢
	proveit.numbers.addition.association
19	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
20	instantiation	25	⊢
	: , :
21	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
22	instantiation	62, 46, 26	⊢
	: , : , :
23	instantiation	27, 28, 29	⊢
	: , : , :
24	instantiation	62, 30, 31	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
26	instantiation	32, 33, 55	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.sub_right_side_into
28	instantiation	34, 38, 35, 36	⊢
	: , : , :
29	instantiation	37, 38, 39	⊢
	: , :
30	instantiation	40, 56, 41	⊢
	: , :
31	assumption		⊢
32	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
33	instantiation	42, 43	⊢
	: , :
34	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add_reversed
35	instantiation	62, 46, 44	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
37	theorem		⊢
	proveit.numbers.addition.commutation
38	instantiation	62, 46, 45	⊢
	: , : , :
39	instantiation	62, 46, 47	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
41	instantiation	48, 49, 58	⊢
	: , :
42	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
44	instantiation	62, 52, 50	⊢
	: , : , :
45	instantiation	62, 52, 51	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
47	instantiation	62, 52, 53	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
49	instantiation	62, 54, 55	⊢
	: , : , :
50	instantiation	62, 57, 61	⊢
	: , : , :
51	instantiation	62, 57, 56	⊢
	: , : , :
52	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
53	instantiation	62, 57, 58	⊢
	: , : , :
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
55	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
56	instantiation	62, 63, 59	⊢
	: , : , :
57	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
58	instantiation	60, 61	⊢
	:
59	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
60	theorem		⊢
	proveit.numbers.negation.int_closure
61	instantiation	62, 63, 64	⊢
	: , : , :
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