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