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	⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
2	instantiation	3, 4	⊢
	: , : , :
3	theorem		⊢
	proveit.logic.sets.functions.bijections.membership_unfolding
4	instantiation	5, 6	⊢
	: , : , :
5	theorem		⊢
	proveit.logic.sets.functions.bijections.elim_domain_condition
6	modus ponens	7, 8	⊢
7	instantiation	9, 10^*	⊢
	: , : , : , : , : , :
8	instantiation	11, 12, 13	⊢
	: , :
9	theorem		⊢
	proveit.logic.sets.functions.bijections.bijection_transitivity
10	instantiation	14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
12	instantiation	16, 17, 31, 36, 24	⊢
	: , : , : , : , :
13	theorem		⊢
	proveit.physics.quantum.QPE._sample_space_bijection
14	axiom		⊢
	proveit.logic.equality.substitution
15	instantiation	18, 19	⊢
	: , :
16	theorem		⊢
	proveit.numbers.modular.interval_left_shift_bijection
17	instantiation	20, 21, 22	⊢
	: , :
18	theorem		⊢
	proveit.logic.equality.equals_reversal
19	instantiation	23, 24, 25	⊢
	: , :
20	theorem		⊢
	proveit.numbers.exponentiation.exp_natpos_closure
21	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
22	instantiation	39, 26, 27	⊢
	: , : , :
23	axiom		⊢
	proveit.physics.quantum.QPE._mod_add_def
24	theorem		⊢
	proveit.physics.quantum.QPE._best_floor_is_int
25	instantiation	39, 28, 29	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
27	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos
28	instantiation	30, 31, 36	⊢
	: , :
29	assumption		⊢
30	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
31	instantiation	32, 33, 34	⊢
	: , :
32	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
33	instantiation	35, 36	⊢
	:
34	instantiation	39, 37, 38	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.negation.int_closure
36	instantiation	39, 40, 41	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
38	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
39	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
40	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
41	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
^*equality replacement requirements