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	generalization	1	⊢
1	instantiation	2, 3, 4, 5	⊢
	: , : , :
2	theorem		⊢
	proveit.numbers.number_sets.real_numbers.all_in_interval_cc__is__real
3	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
4	instantiation	18, 6, 7	⊢
	: , : , :
5	instantiation	8, 9, 10	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
7	instantiation	18, 11, 12	⊢
	: , : , :
8	theorem		⊢
	proveit.logic.equality.sub_left_side_into
9	instantiation	13, 14, 15	⊢
	: , :
10	instantiation	20, 16, 17	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
12	instantiation	18, 19, 35	⊢
	: , : , :
13	theorem		⊢
	proveit.statistics.event_prob_in_interval
14	instantiation	20, 27, 21	⊢
	: , : , :
15	modus ponens	22, 23	⊢
16	instantiation	24, 25	⊢
	:
17	instantiation	26, 27, 28	⊢
	: , : , : , : , :
18	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
19	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
20	theorem		⊢
	proveit.logic.equality.sub_right_side_into
21	axiom		⊢
	proveit.physics.quantum.QPE._sample_space_def
22	instantiation	29, 30, 31^*	⊢
	: , : , : , : , : , : , :
23	generalization	32	⊢
24	axiom		⊢
	proveit.physics.quantum.QPE._fail_def
25	assumption		⊢
26	axiom		⊢
	proveit.statistics.prob_of_all_def
27	theorem		⊢
	proveit.physics.quantum.QPE._Omega_is_sample_space
28	instantiation	40, 33	⊢
	: , :
29	theorem		⊢
	proveit.logic.sets.comprehension.subset_via_condition_constraint
30	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
31	instantiation	34, 35, 36, 37	⊢
	: , : , : , : , :
32	axiom		⊢
	proveit.logic.booleans.true_axiom
33	instantiation	38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.core_expr_types.conditionals.true_condition_elimination
35	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
36	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
37	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
38	theorem		⊢
	proveit.logic.sets.functions.injections.membership_unfolding
39	instantiation	40, 41	⊢
	: , :
40	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
41	instantiation	42, 43	⊢
	: , : , :
42	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
43	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
^*equality replacement requirements