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, 47, 10, 11, 12	⊢
	: , : , : , : , : , : , :
3	instantiation	5, 6, 50, 7, 8, 9, 10, 11, 12, 13^*	⊢
	: , : , : , : , : , :
4	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
5	theorem		⊢
	proveit.numbers.multiplication.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	14	⊢
	: , :
9	instantiation	14	⊢
	: , :
10	instantiation	48, 26, 37	⊢
	: , : , :
11	instantiation	48, 26, 15	⊢
	: , : , :
12	instantiation	48, 26, 16	⊢
	: , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
14	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
15	instantiation	17, 18, 19	⊢
	: , : , :
16	instantiation	48, 20, 21	⊢
	: , : , :
17	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
18	instantiation	22, 23	⊢
	: , :
19	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_is_nat_pos
20	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_nonneg_within_real
21	instantiation	24, 25	⊢
	:
22	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
23	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
24	theorem		⊢
	proveit.numbers.absolute_value.abs_complex_closure
25	instantiation	48, 26, 27	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
27	instantiation	28, 29, 32, 30	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_co__is__real
29	instantiation	31, 32	⊢
	:
30	instantiation	33, 34	⊢
	:
31	theorem		⊢
	proveit.numbers.negation.real_closure
32	instantiation	35, 36, 37, 38	⊢
	: , :
33	theorem		⊢
	proveit.physics.quantum.QPE._delta_b_floor_diff_in_interval
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.division.div_real_closure
36	instantiation	48, 40, 39	⊢
	: , : , :
37	instantiation	48, 40, 41	⊢
	: , : , :
38	instantiation	42, 43	⊢
	:
39	instantiation	48, 45, 44	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	48, 45, 46	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
43	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
44	instantiation	48, 49, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	48, 49, 50	⊢
	: , : , :
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements