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