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