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	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 9, 50, 57, 11, 7, 12, 25, 24	⊢
	: , : , : , : , : , :
5	instantiation	8, 57, 50, 9, 10, 11, 12, 25, 24, 13^*	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.addition.disassociation
7	instantiation	14	⊢
	: , :
8	theorem		⊢
	proveit.numbers.addition.association
9	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
10	instantiation	14	⊢
	: , :
11	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
12	instantiation	55, 29, 15	⊢
	: , : , :
13	instantiation	16, 17, 18	⊢
	: , : , :
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	55, 43, 19	⊢
	: , : , :
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	20, 21, 24, 22	⊢
	: , : , :
18	instantiation	23, 24, 25	⊢
	: , :
19	instantiation	55, 26, 27	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.addition.subtraction.subtract_from_add
21	instantiation	55, 29, 36	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
23	theorem		⊢
	proveit.numbers.addition.commutation
24	instantiation	55, 29, 28	⊢
	: , : , :
25	instantiation	55, 29, 30	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
27	instantiation	31, 32, 33	⊢
	: , :
28	instantiation	55, 43, 34	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	35, 36	⊢
	:
31	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
32	instantiation	55, 37, 38	⊢
	: , : , :
33	instantiation	39, 40, 41	⊢
	: , :
34	instantiation	55, 51, 42	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.negation.real_closure
36	instantiation	55, 43, 44	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
38	instantiation	55, 45, 46	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
40	instantiation	55, 53, 47	⊢
	: , : , :
41	instantiation	48, 49	⊢
	:
42	instantiation	55, 56, 50	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	55, 51, 52	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
47	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
48	theorem		⊢
	proveit.numbers.negation.int_closure
49	instantiation	55, 53, 54	⊢
	: , : , :
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	55, 56, 57	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
54	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos
55	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
56	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
57	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements