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	23	⊢
2	instantiation	4, 5	⊢
	: , : , :
3	instantiation	36, 6	⊢
	:
4	axiom		⊢
	proveit.logic.equality.substitution
5	instantiation	7, 8, 46, 9^*	⊢
	: , : , : , :
6	instantiation	47, 40, 10	⊢
	: , : , :
7	theorem		⊢
	proveit.numbers.addition.rational_pair_addition
8	instantiation	47, 48, 11	⊢
	: , : , :
9	instantiation	23, 12, 13	⊢
	: , : , :
10	instantiation	47, 14, 15	⊢
	: , : , :
11	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
12	instantiation	29, 49, 16, 17, 18, 19	⊢
	: , : , : , :
13	instantiation	20, 21, 22	⊢
	:
14	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
15	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
16	instantiation	35	⊢
	: , :
17	instantiation	35	⊢
	: , :
18	instantiation	23, 24, 25	⊢
	: , : , :
19	theorem		⊢
	proveit.numbers.numerals.decimals.mult_2_2
20	theorem		⊢
	proveit.numbers.division.frac_cancel_complete
21	instantiation	47, 40, 26	⊢
	: , : , :
22	instantiation	27, 28	⊢
	:
23	axiom		⊢
	proveit.logic.equality.equals_transitivity
24	instantiation	29, 49, 30, 31, 32, 33	⊢
	: , : , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_2_2
26	instantiation	47, 43, 34	⊢
	: , : , :
27	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.nonzero_if_is_nat_pos
28	theorem		⊢
	proveit.numbers.numerals.decimals.posnat4
29	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
30	instantiation	35	⊢
	: , :
31	instantiation	35	⊢
	: , :
32	instantiation	36, 38	⊢
	:
33	instantiation	37, 38	⊢
	:
34	instantiation	47, 45, 39	⊢
	: , : , :
35	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
36	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
37	theorem		⊢
	proveit.numbers.multiplication.elim_one_right
38	instantiation	47, 40, 41	⊢
	: , : , :
39	instantiation	47, 48, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
41	instantiation	47, 43, 44	⊢
	: , : , :
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat4
43	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
44	instantiation	47, 45, 46	⊢
	: , : , :
45	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
46	instantiation	47, 48, 49	⊢
	: , : , :
47	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
48	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
49	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
^*equality replacement requirements