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.physics.quantum.circuits.circuit_equiv_temporal_sub
2	reference	80	⊢
3	reference	18	⊢
4	instantiation	24, 5, 63, 6	⊢
	: , : , : , :
5	instantiation	7, 8, 9	⊢
	: , : , :
6	instantiation	10, 11	⊢
	: , :
7	theorem		⊢
	proveit.logic.equality.sub_right_side_into
8	instantiation	12, 13	⊢
	: , : , :
9	instantiation	14, 15, 16	⊢
	: , : , :
10	theorem		⊢
	proveit.logic.equality.equals_reversal
11	instantiation	17, 18	⊢
	: , :
12	theorem		⊢
	proveit.core_expr_types.tuples.range_len
13	instantiation	19, 39, 20, 38, 21, 80	⊢
	: , :
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	22, 23	⊢
	: , : , :
16	instantiation	24, 25, 26, 27	⊢
	: , : , : , :
17	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
18	instantiation	83, 28, 85	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.addition.add_nat_closure
20	instantiation	50	⊢
	: , : , :
21	instantiation	29, 30	⊢
	:
22	axiom		⊢
	proveit.logic.equality.substitution
23	instantiation	31, 60, 59, 32*	⊢
	: , :
24	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
25	instantiation	33, 80, 34, 35, 36, 62, 42, 59	⊢
	: , : , : , : , : , :
26	instantiation	37, 38, 39, 40, 41, 62, 42, 59	⊢
	: , : , : , :
27	instantiation	43, 59, 62, 44	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
29	theorem		⊢
	proveit.numbers.negation.nat_closure
30	instantiation	45, 46, 47	⊢
	:
31	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
32	instantiation	48, 62	⊢
	:
33	theorem		⊢
	proveit.numbers.addition.disassociation
34	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
35	instantiation	49	⊢
	: , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
37	theorem		⊢
	proveit.numbers.addition.elim_zero_any
38	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
40	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
41	instantiation	50	⊢
	: , : , :
42	instantiation	51, 59	⊢
	:
43	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
44	instantiation	68	⊢
	:
45	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
46	instantiation	52, 76, 74	⊢
	: , :
47	instantiation	53, 65, 64, 67, 54, 55*, 56*	⊢
	: , : , :
48	theorem		⊢
	proveit.numbers.negation.double_negation
49	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
50	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
51	theorem		⊢
	proveit.numbers.negation.complex_closure
52	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
53	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
54	instantiation	57, 85	⊢
	:
55	instantiation	58, 59, 60	⊢
	: , :
56	instantiation	61, 62, 63	⊢
	: , :
57	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
58	theorem		⊢
	proveit.numbers.addition.commutation
59	instantiation	83, 66, 64	⊢
	: , : , :
60	instantiation	83, 66, 65	⊢
	: , : , :
61	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
62	instantiation	83, 66, 67	⊢
	: , : , :
63	instantiation	68	⊢
	:
64	instantiation	83, 70, 69	⊢
	: , : , :
65	instantiation	83, 70, 71	⊢
	: , : , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
67	instantiation	72, 73, 85	⊢
	: , : , :
68	axiom		⊢
	proveit.logic.equality.equals_reflexivity
69	instantiation	83, 75, 74	⊢
	: , : , :
70	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
71	instantiation	83, 75, 76	⊢
	: , : , :
72	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
73	instantiation	77, 78	⊢
	: , :
74	instantiation	83, 79, 80	⊢
	: , : , :
75	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
76	instantiation	81, 82	⊢
	:
77	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
78	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
79	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
80	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
81	theorem		⊢
	proveit.numbers.negation.int_closure
82	instantiation	83, 84, 85	⊢
	: , : , :
83	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
84	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
85	assumption		⊢
*equality replacement requirements