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	⊢
	: , : , :
1	axiom		⊢
	proveit.logic.equality.substitution
2	instantiation	3, 4, 5	⊢
	: , : , :
3	axiom		⊢
	proveit.logic.equality.equals_transitivity
4	instantiation	6, 21, 42, 22, 23, 7, 10, 26, 8	⊢
	: , : , : , : , : , :
5	instantiation	9, 26, 10, 11	⊢
	: , : , :
6	theorem		⊢
	proveit.numbers.addition.disassociation
7	instantiation	29	⊢
	: , :
8	instantiation	40, 32, 12	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
10	instantiation	40, 32, 13	⊢
	: , : , :
11	instantiation	14	⊢
	:
12	instantiation	15, 31	⊢
	:
13	instantiation	16, 17, 18	⊢
	: , : , :
14	axiom		⊢
	proveit.logic.equality.equals_reflexivity
15	theorem		⊢
	proveit.numbers.negation.real_closure
16	theorem		⊢
	proveit.logic.equality.sub_right_side_into
17	instantiation	28, 19, 33	⊢
	: , :
18	instantiation	20, 21, 42, 22, 23, 24, 25, 26, 27	⊢
	: , : , : , : , : , :
19	instantiation	28, 30, 31	⊢
	: , :
20	theorem		⊢
	proveit.numbers.multiplication.disassociation
21	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
22	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
23	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
24	instantiation	29	⊢
	: , :
25	instantiation	40, 32, 30	⊢
	: , : , :
26	instantiation	40, 32, 31	⊢
	: , : , :
27	instantiation	40, 32, 33	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.multiplication.mult_real_closure_bin
29	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
30	instantiation	40, 34, 35	⊢
	: , : , :
31	instantiation	40, 36, 37	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	40, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat2