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, 4^*	, , ⊢
	: , :
1	axiom		⊢
	proveit.linear_algebra.scalar_multiplication.scalar_mult_extends_number_mult
2	instantiation	42, 24, 5	, ⊢
	: , : , :
3	reference	10	, ⊢
4	instantiation	6, 7, 8	, , ⊢
	: , : , :
5	instantiation	9, 22, 27	, ⊢
	: , :
6	axiom		⊢
	proveit.logic.equality.equals_transitivity
7	instantiation	11, 12, 41, 37, 15, 13, 16, 17, 10	, , ⊢
	: , : , : , : , : , :
8	instantiation	11, 41, 12, 13, 14, 15, 16, 17, 19, 20	, , ⊢
	: , : , : , : , : , :
9	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
10	instantiation	18, 19, 20	, ⊢
	: , :
11	theorem		⊢
	proveit.numbers.multiplication.disassociation
12	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
13	instantiation	21	⊢
	: , :
14	instantiation	21	⊢
	: , :
15	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
16	instantiation	42, 24, 22	⊢
	: , : , :
17	instantiation	42, 24, 27	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
19	instantiation	42, 24, 23	⊢
	: , : , :
20	instantiation	42, 24, 25	⊢
	: , : , :
21	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
22	assumption		⊢
23	assumption		⊢
24	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
25	instantiation	26, 27, 28	⊢
	: , :
26	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
27	instantiation	42, 30, 29	⊢
	: , : , :
28	instantiation	42, 30, 31	⊢
	: , : , :
29	instantiation	42, 33, 32	⊢
	: , : , :
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
31	instantiation	42, 33, 34	⊢
	: , : , :
32	instantiation	42, 35, 36	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
34	instantiation	42, 43, 37	⊢
	: , : , :
35	instantiation	38, 39, 40	⊢
	: , :
36	assumption		⊢
37	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
38	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
39	instantiation	42, 43, 41	⊢
	: , : , :
40	instantiation	42, 43, 44	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
43	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
44	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
^*equality replacement requirements