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	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 10, 46, 43, 12, 7, 14, 15, 13, 16	⊢
	: , : , : , : , : , : , :
5	instantiation	8, 43, 9, 10, 11, 12, 13, 14, 15, 16	⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	instantiation	17	⊢
	: , :
8	theorem		⊢
	proveit.numbers.multiplication.association
9	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
10	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
11	instantiation	18	⊢
	: , : , :
12	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
13	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
14	instantiation	44, 20, 33	⊢
	: , : , :
15	instantiation	44, 20, 19	⊢
	: , : , :
16	instantiation	44, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
18	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
19	instantiation	44, 22, 23	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
21	instantiation	24, 25, 28, 26	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
24	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
25	instantiation	27, 28	⊢
	:
26	instantiation	29, 30	⊢
	:
27	theorem		⊢
	proveit.numbers.negation.real_closure
28	instantiation	31, 32, 33, 34	⊢
	: , :
29	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
30	assumption		⊢
31	theorem		⊢
	proveit.numbers.division.div_real_closure
32	instantiation	44, 36, 35	⊢
	: , : , :
33	instantiation	44, 36, 37	⊢
	: , : , :
34	instantiation	38, 39	⊢
	:
35	instantiation	44, 41, 40	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	44, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	instantiation	44, 45, 43	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	44, 45, 46	⊢
	: , : , :
43	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
44	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
45	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
46	theorem		⊢
	proveit.numbers.numerals.decimals.nat2