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	21	⊢
2	instantiation	21, 4, 5	, , ⊢
	: , : , :
3	instantiation	7, 6	, , ⊢
	: , : , :
4	instantiation	7, 8	, ⊢
	: , : , :
5	instantiation	9, 15, 14, 46	, , ⊢
	: , : , :
6	instantiation	10, 24, 41, 11, 44, 12	, , ⊢
	: , : , : , :
7	axiom		⊢
	proveit.logic.equality.substitution
8	instantiation	13, 14, 15	, ⊢
	: , :
9	theorem		⊢
	proveit.numbers.exponentiation.pos_power_of_product
10	theorem		⊢
	proveit.numbers.exponentiation.exp_factored_real
11	instantiation	16, 41, 39	, ⊢
	: , :
12	instantiation	17, 18	, ⊢
	: , :
13	theorem		⊢
	proveit.numbers.multiplication.commutation
14	instantiation	49, 40, 19	⊢
	: , : , :
15	instantiation	49, 40, 20	⊢
	: , : , :
16	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
17	theorem		⊢
	proveit.logic.equality.equals_reversal
18	instantiation	21, 22, 23	, ⊢
	: , : , :
19	instantiation	49, 45, 24	⊢
	: , : , :
20	instantiation	49, 47, 25	⊢
	: , : , :
21	axiom		⊢
	proveit.logic.equality.equals_transitivity
22	instantiation	26, 27, 28, 29, 30, 31, 35, 32, 34	, ⊢
	: , : , : , : , : , :
23	instantiation	33, 34, 35, 36	, ⊢
	: , : , :
24	assumption		⊢
25	instantiation	49, 50, 37	⊢
	: , : , :
26	theorem		⊢
	proveit.numbers.addition.disassociation
27	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
28	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
29	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
30	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
31	instantiation	38	⊢
	: , :
32	instantiation	49, 40, 39	⊢
	: , : , :
33	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
34	instantiation	49, 40, 44	⊢
	: , : , :
35	instantiation	49, 40, 41	⊢
	: , : , :
36	instantiation	42	⊢
	:
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
39	instantiation	43, 44	⊢
	:
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	49, 45, 46	⊢
	: , : , :
42	axiom		⊢
	proveit.logic.equality.equals_reflexivity
43	theorem		⊢
	proveit.numbers.negation.real_closure
44	instantiation	49, 47, 48	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
46	assumption		⊢
47	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
48	instantiation	49, 50, 51	⊢
	: , : , :
49	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
50	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
51	assumption		⊢