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, 4, 5, 6	⊢
	: , : , : , :
1	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
2	reference	32	⊢
3	instantiation	19	⊢
	: , :
4	instantiation	19	⊢
	: , :
5	instantiation	7, 8, 9	⊢
	: , : , :
6	instantiation	10, 16	⊢
	:
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	11, 51, 32, 14, 12, 15, 16, 17, 18	⊢
	: , : , : , : , : , :
9	instantiation	13, 14, 51, 15, 16, 17, 18	⊢
	: , : , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
11	theorem		⊢
	proveit.numbers.multiplication.disassociation
12	instantiation	19	⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
14	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	49, 22, 20	⊢
	: , : , :
17	instantiation	49, 22, 21	⊢
	: , : , :
18	instantiation	49, 22, 36	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
20	instantiation	23, 24, 43	⊢
	: , :
21	instantiation	49, 45, 25	⊢
	: , : , :
22	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
23	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
24	instantiation	49, 26, 27	⊢
	: , : , :
25	instantiation	49, 47, 28	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
27	instantiation	29, 30, 31	⊢
	: , :
28	instantiation	49, 50, 32	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.multiplication.mult_real_pos_closure_bin
30	instantiation	49, 33, 34	⊢
	: , : , :
31	instantiation	35, 36, 37	⊢
	:
32	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
33	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_pos_within_real_pos
34	instantiation	49, 38, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
36	instantiation	40, 42, 43, 44	⊢
	: , : , :
37	instantiation	41, 42, 43, 44	⊢
	: , : , :
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.nat_pos_within_rational_pos
39	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_oc__is__real
41	theorem		⊢
	proveit.numbers.number_sets.real_numbers.interval_oc_lower_bound
42	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
43	instantiation	49, 45, 46	⊢
	: , : , :
44	axiom		⊢
	proveit.physics.quantum.QPE._eps_in_interval
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
46	instantiation	49, 47, 48	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
51	theorem		⊢
	proveit.numbers.numerals.decimals.nat1