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	7	⊢
2	instantiation	10, 4	, ⊢
	: , : , :
3	instantiation	7, 5, 6	, ⊢
	: , : , :
4	instantiation	7, 8, 9	, ⊢
	: , : , :
5	instantiation	10, 11	, ⊢
	: , : , :
6	instantiation	12, 29, 40	, ⊢
	: , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	13, 41, 15, 16, 18, 23, 19	, ⊢
	: , : , : , : , : , : , :
9	instantiation	14, 15, 42, 41, 16, 17, 18, 19, 23, 20^*	, ⊢
	: , : , : , : , : , :
10	axiom		⊢
	proveit.logic.equality.substitution
11	instantiation	21, 22, 23	, ⊢
	: , :
12	theorem		⊢
	proveit.numbers.rounding.round_of_real_plus_int
13	theorem		⊢
	proveit.numbers.addition.leftward_commutation
14	theorem		⊢
	proveit.numbers.addition.association
15	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
16	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
17	instantiation	24	⊢
	: , :
18	instantiation	43, 28, 25	⊢
	: , : , :
19	instantiation	43, 28, 26	⊢
	: , : , :
20	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_2
21	theorem		⊢
	proveit.numbers.addition.commutation
22	instantiation	43, 28, 27	⊢
	: , : , :
23	instantiation	43, 28, 29	, ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
25	instantiation	43, 32, 30	⊢
	: , : , :
26	instantiation	43, 32, 31	⊢
	: , : , :
27	instantiation	43, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
29	instantiation	34, 35, 36	, ⊢
	: , :
30	instantiation	43, 39, 37	⊢
	: , : , :
31	instantiation	43, 39, 38	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
33	instantiation	43, 39, 40	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
35	assumption		⊢
36	assumption		⊢
37	instantiation	43, 44, 41	⊢
	: , : , :
38	instantiation	43, 44, 42	⊢
	: , : , :
39	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
40	instantiation	43, 44, 45	⊢
	: , : , :
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
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.nat3
^*equality replacement requirements