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.logic.equality.equals_transitivity
2	instantiation	5, 6	, ⊢
	: , : , :
3	instantiation	7, 8	, ⊢
	: , :
4	instantiation	9, 30, 23, 47, 24, 25, 26, 27, 10	, ⊢
	: , : , : , : , : , :
5	axiom		⊢
	proveit.logic.equality.substitution
6	modus ponens	11, 12	, ⊢
7	theorem		⊢
	proveit.logic.equality.equals_reversal
8	instantiation	13, 24, 14	, ⊢
	: , :
9	theorem		⊢
	proveit.numbers.multiplication.disassociation
10	modus ponens	15, 19	⊢
11	instantiation	16, 29	⊢
	: , : , : , : , : , : , :
12	generalization	17	, ⊢
13	modus ponens	18, 19	⊢
14	instantiation	20, 26, 27	, ⊢
	: , :
15	instantiation	21	⊢
	: , : , :
16	theorem		⊢
	proveit.core_expr_types.lambda_maps.general_lambda_substitution
17	instantiation	22, 30, 23, 47, 24, 25, 26, 27, 31	, , ⊢
	: , : , : , : , : , :
18	instantiation	28, 47, 29, 30	⊢
	: , : , : , : , : , :
19	generalization	31	⊢
20	theorem		⊢
	proveit.numbers.multiplication.mult_complex_closure_bin
21	theorem		⊢
	proveit.numbers.summation.summation_complex_closure
22	theorem		⊢
	proveit.numbers.multiplication.association
23	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
24	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
25	instantiation	32	⊢
	: , :
26	assumption		⊢
27	assumption		⊢
28	theorem		⊢
	proveit.numbers.multiplication.distribute_through_summation
29	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
30	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
31	instantiation	33, 34, 35	⊢
	: , :
32	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
33	theorem		⊢
	proveit.numbers.addition.add_complex_closure_bin
34	instantiation	45, 37, 36	⊢
	: , : , :
35	instantiation	45, 37, 38	⊢
	: , : , :
36	instantiation	45, 40, 39	⊢
	: , : , :
37	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
38	instantiation	45, 40, 41	⊢
	: , : , :
39	instantiation	45, 43, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
41	instantiation	45, 43, 44	⊢
	: , : , :
42	assumption		⊢
43	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
44	instantiation	45, 46, 47	⊢
	: , : , :
45	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
46	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
47	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements