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, 5, 6, 32, 7, 8, 12, 11, 9	⊢
	: , : , : , : , : , :
3	instantiation	10, 11, 12, 13	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
6	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
7	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
8	instantiation	14	⊢
	: , :
9	instantiation	43, 16, 15	⊢
	: , : , :
10	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
11	instantiation	43, 16, 20	⊢
	: , : , :
12	instantiation	43, 16, 17	⊢
	: , : , :
13	instantiation	18	⊢
	:
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	19, 20	⊢
	:
16	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
17	instantiation	43, 22, 21	⊢
	: , : , :
18	axiom		⊢
	proveit.logic.equality.equals_reflexivity
19	theorem		⊢
	proveit.numbers.negation.real_closure
20	instantiation	43, 22, 23	⊢
	: , : , :
21	instantiation	43, 24, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
23	instantiation	43, 26, 27	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.rational_nonzero_within_rational
25	instantiation	28, 29, 30	⊢
	: , :
26	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
27	instantiation	43, 31, 32	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.exponentiation.exp_rational_nonzero_closure
29	instantiation	43, 33, 34	⊢
	: , : , :
30	instantiation	35, 36, 37	⊢
	: , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nonzero_int_within_rational_nonzero
34	instantiation	43, 38, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
36	instantiation	43, 44, 40	⊢
	: , : , :
37	instantiation	41, 42	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_nonzero_int
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
41	theorem		⊢
	proveit.numbers.negation.int_closure
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
45	axiom		⊢
	proveit.physics.quantum.QPE._n_in_natural_pos