Show the Proof

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

	step type	requirements	statement
0	instantiation	1, 2, 3, 4	, ,  ⊢
	: , :
1	theorem		⊢
	proveit.logic.booleans.disjunction.any_if_all
2	reference	40	⊢
3	instantiation	5, 6	⊢
	: , :
4	modus ponens	7, 8	, ,  ⊢
5	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
6	instantiation	38, 9, 40	⊢
	: , : , :
7	instantiation	10, 33, 34, 11	⊢
	: , : , : , :
8	generalization	12	, ,  ⊢
9	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
10	theorem		⊢
	proveit.logic.booleans.conjunction.conjunction_from_quantification
11	instantiation	13, 14	⊢
	:
12	instantiation	15, 16, 17	, , ,  ⊢
	: , : , : , :
13	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
14	instantiation	18, 40, 19	⊢
	: , :
15	theorem		⊢
	proveit.physics.quantum.circuits.qcircuit_output_part_neq
16	instantiation	20, 21, 22	⊢
	:
17	instantiation	23, 40, 24, 25, 26	, ,  ⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
19	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
20	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
21	instantiation	38, 27, 35	⊢
	: , : , :
22	instantiation	28, 29, 30	⊢
	: , : , :
23	theorem		⊢
	proveit.physics.quantum.algebra.num_ket_neq
24	assumption		⊢
25	assumption		⊢
26	assumption		⊢
27	instantiation	31, 33, 34	⊢
	: , :
28	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
29	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
30	instantiation	32, 33, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
32	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
33	instantiation	38, 36, 37	⊢
	: , : , :
34	instantiation	38, 39, 40	⊢
	: , : , :
35	assumption		⊢
36	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
39	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
40	axiom		⊢
	proveit.physics.quantum.QPE._t_in_natural_pos