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, 5*	⊢
	: , : , :
1	theorem		⊢
	proveit.linear_algebra.tensors.tensor_prod_of_cart_exps_within_cart_exp
2	reference	136	⊢
3	instantiation	49, 6, 113, 7	⊢
	: , : , : , :
4	instantiation	8, 87, 9, 10, 11	⊢
	: , : , :
5	instantiation	12, 13, 14, 18, 15*, 18*	⊢
	: , :
6	instantiation	16, 17, 18	⊢
	: , : , :
7	instantiation	62, 19	⊢
	: , :
8	theorem		⊢
	proveit.logic.booleans.conjunction.redundant_conjunction_general
9	theorem		⊢
	proveit.numbers.number_sets.integers.zero_is_int
10	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
11	instantiation	96, 20, 21, 118, 22, 23*, 24*	⊢
	: , : , :
12	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_rev
13	instantiation	84, 102, 101, 25, 103, 60, 131, 85	⊢
	: , : , : , : , :
14	instantiation	134, 117, 26	⊢
	: , : , :
15	instantiation	62, 27	⊢
	: , :
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	28, 29	⊢
	: , : , :
18	instantiation	89, 30, 31	⊢
	: , : , :
19	instantiation	32, 33	⊢
	: , :
20	instantiation	134, 121, 34	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.number_sets.real_numbers.zero_is_real
22	instantiation	35, 36	⊢
	: , :
23	instantiation	89, 37, 38	⊢
	: , : , :
24	instantiation	49, 39, 72, 40	⊢
	: , : , : , :
25	instantiation	114	⊢
	: , :
26	instantiation	134, 121, 41	⊢
	: , : , :
27	instantiation	42, 127, 43, 44, 45	⊢
	: , : , : , : , : , :
28	theorem		⊢
	proveit.core_expr_types.tuples.range_len
29	instantiation	46, 68, 47, 101, 60, 131	⊢
	: , :
30	instantiation	92, 48	⊢
	: , : , :
31	instantiation	49, 50, 51, 52	⊢
	: , : , : , :
32	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len
33	instantiation	134, 74, 136	⊢
	: , : , :
34	instantiation	134, 126, 87	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.ordering.relax_less
36	instantiation	53, 136	⊢
	:
37	instantiation	100, 131, 102, 101, 104, 103, 66, 110, 109	⊢
	: , : , : , : , : , :
38	instantiation	67, 101, 102, 103, 104, 110, 109	⊢
	: , : , : , :
39	instantiation	89, 54, 55	⊢
	: , : , :
40	instantiation	62, 56	⊢
	: , :
41	instantiation	134, 126, 57	⊢
	: , : , :
42	theorem		⊢
	proveit.core_expr_types.tuples.shift_equivalence
43	instantiation	58, 59, 60	⊢
	: , :
44	instantiation	62, 61	⊢
	: , :
45	instantiation	62, 63	⊢
	: , :
46	theorem		⊢
	proveit.numbers.addition.add_nat_closure
47	instantiation	82	⊢
	: , : , :
48	instantiation	64, 110, 109, 93*	⊢
	: , :
49	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
50	instantiation	100, 131, 102, 65, 66, 112, 70, 109	⊢
	: , : , : , : , : , :
51	instantiation	67, 101, 68, 103, 69, 112, 70, 109	⊢
	: , : , : , :
52	instantiation	71, 109, 112, 72	⊢
	: , : , :
53	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
54	instantiation	100, 131, 102, 101, 104, 103, 112, 110, 109	⊢
	: , : , : , : , : , :
55	instantiation	73, 112, 109, 113	⊢
	: , : , :
56	instantiation	94, 109	⊢
	:
57	instantiation	134, 130, 102	⊢
	: , : , :
58	theorem		⊢
	proveit.numbers.addition.add_nat_closure_bin
59	instantiation	134, 74, 75	⊢
	: , : , :
60	instantiation	76, 77	⊢
	:
61	instantiation	89, 78, 79	⊢
	: , : , :
62	theorem		⊢
	proveit.logic.equality.equals_reversal
63	instantiation	89, 80, 81	⊢
	: , : , :
64	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
65	instantiation	114	⊢
	: , :
66	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.zero_is_complex
67	theorem		⊢
	proveit.numbers.addition.elim_zero_any
68	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
69	instantiation	82	⊢
	: , : , :
70	instantiation	83, 109	⊢
	:
71	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
72	instantiation	119	⊢
	:
73	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
74	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nat_pos_within_nat
75	instantiation	84, 131, 101, 103, 85	⊢
	: , : , : , : , :
76	theorem		⊢
	proveit.numbers.negation.nat_closure
77	instantiation	86, 87, 88	⊢
	:
78	instantiation	92, 93	⊢
	: , : , :
79	instantiation	89, 90, 91	⊢
	: , : , :
80	instantiation	92, 93	⊢
	: , : , :
81	instantiation	94, 112	⊢
	:
82	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
83	theorem		⊢
	proveit.numbers.negation.complex_closure
84	theorem		⊢
	proveit.numbers.addition.add_nat_pos_from_nonneg
85	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
86	theorem		⊢
	proveit.numbers.number_sets.integers.nonpos_int_is_int_nonpos
87	instantiation	95, 127, 125	⊢
	: , :
88	instantiation	96, 116, 115, 118, 97, 98*, 99*	⊢
	: , : , :
89	axiom		⊢
	proveit.logic.equality.equals_transitivity
90	instantiation	100, 101, 102, 131, 103, 104, 110, 109, 112	⊢
	: , : , : , : , : , :
91	instantiation	105, 112, 109, 113	⊢
	: , : , :
92	axiom		⊢
	proveit.logic.equality.substitution
93	instantiation	106, 112	⊢
	:
94	theorem		⊢
	proveit.numbers.addition.elim_zero_left
95	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
96	theorem		⊢
	proveit.numbers.addition.weak_bound_via_left_term_bound
97	instantiation	107, 136	⊢
	:
98	instantiation	108, 109, 110	⊢
	: , :
99	instantiation	111, 112, 113	⊢
	: , :
100	theorem		⊢
	proveit.numbers.addition.disassociation
101	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
102	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
103	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
104	instantiation	114	⊢
	: , :
105	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_31
106	theorem		⊢
	proveit.numbers.negation.double_negation
107	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_lower_bound
108	theorem		⊢
	proveit.numbers.addition.commutation
109	instantiation	134, 117, 115	⊢
	: , : , :
110	instantiation	134, 117, 116	⊢
	: , : , :
111	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
112	instantiation	134, 117, 118	⊢
	: , : , :
113	instantiation	119	⊢
	:
114	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
115	instantiation	134, 121, 120	⊢
	: , : , :
116	instantiation	134, 121, 122	⊢
	: , : , :
117	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
118	instantiation	123, 124, 136	⊢
	: , : , :
119	axiom		⊢
	proveit.logic.equality.equals_reflexivity
120	instantiation	134, 126, 125	⊢
	: , : , :
121	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
122	instantiation	134, 126, 127	⊢
	: , : , :
123	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
124	instantiation	128, 129	⊢
	: , :
125	instantiation	134, 130, 131	⊢
	: , : , :
126	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
127	instantiation	132, 133	⊢
	:
128	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
129	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
130	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
131	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
132	theorem		⊢
	proveit.numbers.negation.int_closure
133	instantiation	134, 135, 136	⊢
	: , : , :
134	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
135	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
136	assumption		⊢
*equality replacement requirements