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