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