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