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, 4, 5, 6^, 7^	, ⊢
	: , : , :
1	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
2	instantiation	8, 33	⊢
	:
3	reference	33	⊢
4	instantiation	9, 30, 33	⊢
	: , :
5	instantiation	10, 33, 30, 11, 12	, ⊢
	: , : , :
6	instantiation	13, 29, 26	⊢
	: , :
7	instantiation	14, 15, 16	⊢
	: , : , :
8	theorem		⊢
	proveit.numbers.negation.real_closure
9	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
10	theorem		⊢
	proveit.numbers.ordering.less_add_right
11	assumption		⊢
12	instantiation	17, 40	⊢
	:
13	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_basic
14	axiom		⊢
	proveit.logic.equality.equals_transitivity
15	instantiation	18, 19, 40, 20, 21, 22, 25, 29, 23	⊢
	: , : , : , : , : , :
16	instantiation	24, 29, 25, 26	⊢
	: , : , :
17	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_lower_bound
18	theorem		⊢
	proveit.numbers.addition.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	28, 29	⊢
	:
24	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_23
25	instantiation	38, 32, 30	⊢
	: , : , :
26	instantiation	31	⊢
	:
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	theorem		⊢
	proveit.numbers.negation.complex_closure
29	instantiation	38, 32, 33	⊢
	: , : , :
30	assumption		⊢
31	axiom		⊢
	proveit.logic.equality.equals_reflexivity
32	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
33	instantiation	38, 34, 35	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	38, 36, 37	⊢
	: , : , :
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
^*equality replacement requirements