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	7, 3, 4	⊢
	: , : , :
3	instantiation	5, 12, 29, 44, 13, 6, 15, 17, 16	⊢
	: , : , : , : , : , :
4	instantiation	7, 8, 9	⊢
	: , : , :
5	theorem		⊢
	proveit.numbers.addition.disassociation
6	instantiation	19	⊢
	: , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	10, 44, 12, 13, 15, 17, 16	⊢
	: , : , : , : , : , : , :
9	instantiation	11, 12, 29, 44, 13, 14, 15, 16, 17, 18^*	⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.addition.leftward_commutation
11	theorem		⊢
	proveit.numbers.addition.association
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
14	instantiation	19	⊢
	: , :
15	instantiation	42, 21, 20	⊢
	: , : , :
16	instantiation	42, 21, 36	⊢
	: , : , :
17	instantiation	42, 21, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_1
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	instantiation	42, 38, 23	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
22	instantiation	24, 36, 31, 25	⊢
	: , :
23	instantiation	42, 40, 26	⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.division.div_real_closure
25	instantiation	27, 28	⊢
	: , :
26	instantiation	42, 43, 29	⊢
	: , : , :
27	theorem		⊢
	proveit.logic.equality.not_equals_symmetry
28	instantiation	30, 35, 31, 32	⊢
	: , :
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
30	theorem		⊢
	proveit.numbers.ordering.less_is_not_eq
31	instantiation	33, 35, 36, 37	⊢
	: , : , :
32	instantiation	34, 35, 36, 37	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
36	instantiation	42, 38, 39	⊢
	: , : , :
37	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
38	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
39	instantiation	42, 40, 41	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
41	instantiation	42, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements