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	9	⊢
2	instantiation	16, 4	⊢
	: , : , :
3	instantiation	5, 6, 7, 8	, ⊢
	: , : , :
4	instantiation	9, 10, 11	⊢
	: , : , :
5	theorem		⊢
	proveit.linear_algebra.scalar_multiplication.one_as_scalar_mult_id
6	instantiation	43, 33, 12	⊢
	: , : , :
7	instantiation	13, 23	⊢
	:
8	instantiation	14, 15	⊢
	:
9	axiom		⊢
	proveit.logic.equality.equals_transitivity
10	instantiation	16, 17	⊢
	: , : , :
11	instantiation	18, 19	⊢
	:
12	instantiation	43, 37, 20	⊢
	: , : , :
13	assumption		⊢
14	theorem		⊢
	proveit.linear_algebra.complex_vec_set_is_vec_space
15	assumption		⊢
16	axiom		⊢
	proveit.logic.equality.substitution
17	instantiation	21, 22, 23, 24, 25, 26, 27, 28	⊢
	: , : , : , :
18	theorem		⊢
	proveit.numbers.exponentiation.exp_zero_eq_one
19	instantiation	43, 33, 29	⊢
	: , : , :
20	instantiation	43, 41, 30	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.multiplication.mult_zero_any
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
23	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
24	instantiation	31	⊢
	: , : , :
25	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
26	instantiation	43, 33, 32	⊢
	: , : , :
27	instantiation	43, 33, 34	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.i_is_complex
29	instantiation	43, 39, 35	⊢
	: , : , :
30	instantiation	43, 44, 36	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
32	instantiation	43, 37, 38	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
34	instantiation	43, 39, 40	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.number_sets.real_numbers.e_is_real_pos
36	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
38	instantiation	43, 41, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
41	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
42	instantiation	43, 44, 45	⊢
	: , : , :
43	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
44	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
45	theorem		⊢
	proveit.numbers.numerals.decimals.nat2