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, 45, 8, 7, 10, 9, 5, 11, 12	⊢
	: , : , : , : , : , :
3	instantiation	6, 7, 8, 9, 10, 11, 12	⊢
	: , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.disassociation
5	instantiation	43, 21, 31	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.multiplication.elim_one_any
7	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
8	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
9	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
10	instantiation	13	⊢
	: , :
11	instantiation	43, 21, 14	⊢
	: , : , :
12	instantiation	15, 16, 17	⊢
	: , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
14	instantiation	43, 18, 19	⊢
	: , : , :
15	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
16	instantiation	43, 21, 20	⊢
	: , : , :
17	instantiation	43, 21, 22	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
19	instantiation	23, 24, 25, 26	⊢
	: , :
20	instantiation	27, 28, 31, 29	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
22	instantiation	30, 31	⊢
	:
23	theorem		⊢
	proveit.numbers.division.div_real_pos_closure
24	instantiation	43, 33, 32	⊢
	: , : , :
25	instantiation	43, 33, 34	⊢
	: , : , :
26	instantiation	35, 40	⊢
	:
27	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
29	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
30	theorem		⊢
	proveit.numbers.negation.real_closure
31	instantiation	43, 36, 37	⊢
	: , : , :
32	instantiation	43, 39, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
34	instantiation	43, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
37	instantiation	43, 41, 42	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
40	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat1