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, 3	, , , , , ⊢
	: , : , :
1	reference	8	⊢
2	instantiation	8, 4, 5	, , , , , ⊢
	: , : , :
3	instantiation	6, 17, 39, 19, 7, 30, 42, 21, 22	, , , ⊢
	: , : , : , : , : , : , :
4	instantiation	8, 9, 10	, , , , , ⊢
	: , : , :
5	instantiation	16, 17, 24, 19, 11, 18, 30, 42, 21, 22	, , , ⊢
	: , : , : , : , : , :
6	theorem		⊢
	proveit.numbers.multiplication.leftward_commutation
7	instantiation	46	⊢
	: , : , :
8	axiom		⊢
	proveit.logic.equality.equals_transitivity
9	instantiation	12, 20, 13, 14, 15^*	, , , , , ⊢
	: , :
10	instantiation	16, 55, 24, 17, 18, 19, 20, 21, 22	, , , ⊢
	: , : , : , : , : , :
11	instantiation	33	⊢
	: , :
12	theorem		⊢
	proveit.numbers.division.div_as_mult
13	instantiation	29, 41, 36	, ⊢
	: , :
14	instantiation	23, 24, 25, 26, 27	, , , ⊢
	: , :
15	instantiation	28, 41, 36, 45, 34, 37	, , , ⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.multiplication.disassociation
17	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
18	instantiation	33	⊢
	: , :
19	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
20	instantiation	29, 30, 42	, , ⊢
	: , :
21	instantiation	31, 41, 32	⊢
	: , :
22	instantiation	31, 36, 32	⊢
	: , :
23	theorem		⊢
	proveit.numbers.multiplication.mult_not_eq_zero
24	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
25	instantiation	33	⊢
	: , :
26	instantiation	35, 41, 34	, ⊢
	:
27	instantiation	35, 36, 37	, ⊢
	:
28	theorem		⊢
	proveit.numbers.exponentiation.real_power_of_product
29	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
30	instantiation	38, 39, 40, 41, 42, 43	, , ⊢
	: , :
31	theorem		⊢
	proveit.numbers.exponentiation.exp_complex_closure
32	instantiation	53, 44, 45	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
34	assumption		⊢
35	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.nonzero_complex_is_complex_nonzero
36	assumption		⊢
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.addition.add_complex_closure
39	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
40	instantiation	46	⊢
	: , : , :
41	assumption		⊢
42	assumption		⊢
43	assumption		⊢
44	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
45	instantiation	47, 48	⊢
	:
46	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
47	theorem		⊢
	proveit.numbers.negation.real_closure
48	instantiation	53, 49, 50	⊢
	: , : , :
49	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
50	instantiation	53, 51, 52	⊢
	: , : , :
51	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
52	instantiation	53, 54, 55	⊢
	: , : , :
53	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
54	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
55	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements