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	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pos_real_is_real_pos
2	instantiation	4, 12, 41	⊢
	: , :
3	instantiation	5, 6	⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.exponentiation.exp_real_closure_nat_power
5	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
6	instantiation	19, 7, 8	⊢
	: , :
7	instantiation	22, 9	⊢
	:
8	instantiation	10, 11, 39, 12, 13, 14, 15^*	⊢
	: , : , :
9	theorem		⊢
	proveit.numbers.numerals.decimals.posnat9
10	theorem		⊢
	proveit.numbers.exponentiation.exp_pos_less
11	instantiation	48, 44, 16	⊢
	: , : , :
12	instantiation	48, 17, 18	⊢
	: , : , :
13	instantiation	19, 20, 21	⊢
	: , :
14	instantiation	22, 32	⊢
	:
15	instantiation	23, 24, 25, 26	⊢
	: , : , : , :
16	instantiation	48, 46, 27	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.real_numbers.real_pos_within_real
18	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_is_real_pos
19	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
20	instantiation	28, 50	⊢
	:
21	instantiation	29, 30	⊢
	: , :
22	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
23	theorem		⊢
	proveit.logic.equality.four_chain_transitivity
24	instantiation	31, 32, 33	⊢
	: , :
25	instantiation	34, 41, 35, 36, 37	⊢
	: , : , : , :
26	theorem		⊢
	proveit.numbers.numerals.decimals.mult_3_3
27	instantiation	48, 49, 41	⊢
	: , : , :
28	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
29	theorem		⊢
	proveit.logic.booleans.conjunction.left_from_and
30	theorem		⊢
	proveit.numbers.number_sets.real_numbers.pi_between_3_and_4
31	theorem		⊢
	proveit.numbers.exponentiation.exp_nat_pos_expansion
32	theorem		⊢
	proveit.numbers.numerals.decimals.posnat2
33	instantiation	48, 38, 39	⊢
	: , : , :
34	theorem		⊢
	proveit.core_expr_types.operations.operands_substitution_via_tuple
35	instantiation	40, 41	⊢
	: , :
36	instantiation	42	⊢
	: , :
37	instantiation	43	⊢
	:
38	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
39	instantiation	48, 44, 45	⊢
	: , : , :
40	theorem		⊢
	proveit.core_expr_types.tuples.range_from1_len_typical_eq
41	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
42	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
43	theorem		⊢
	proveit.numbers.numerals.decimals.reduce_2_repeats
44	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
45	instantiation	48, 46, 47	⊢
	: , : , :
46	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
47	instantiation	48, 49, 50	⊢
	: , : , :
48	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
49	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
50	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
^*equality replacement requirements