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	10	⊢
2	instantiation	4, 5, 6, 7, 8, 9	⊢
	: , : , : , :
3	instantiation	10, 11, 12	⊢
	: , : , :
4	axiom		⊢
	proveit.core_expr_types.operations.operands_substitution
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
6	instantiation	13	⊢
	: , : , :
7	instantiation	13	⊢
	: , : , :
8	instantiation	14, 24, 16	⊢
	: , : , :
9	instantiation	15, 24, 23, 16	⊢
	: , : , :
10	axiom		⊢
	proveit.logic.equality.equals_transitivity
11	instantiation	17, 20, 19, 22, 21, 24, 23	⊢
	: , : , : , : , : , : , :
12	instantiation	18, 42, 19, 20, 21, 22, 23, 24, 25^*	⊢
	: , : , : , : , : , :
13	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
14	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_12
15	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
16	instantiation	26	⊢
	:
17	theorem		⊢
	proveit.numbers.addition.leftward_commutation
18	theorem		⊢
	proveit.numbers.addition.association
19	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
20	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
21	instantiation	27	⊢
	: , :
22	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
23	instantiation	40, 29, 28	⊢
	: , : , :
24	instantiation	40, 29, 30	⊢
	: , : , :
25	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
26	axiom		⊢
	proveit.logic.equality.equals_reflexivity
27	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
28	instantiation	31, 32, 33	⊢
	: , : , :
29	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
30	instantiation	40, 34, 35	⊢
	: , : , :
31	theorem		⊢
	proveit.logic.sets.inclusion.unfold_subset_eq
32	instantiation	36, 37	⊢
	: , :
33	assumption		⊢
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	40, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.logic.sets.inclusion.relax_proper_subset
37	theorem		⊢
	proveit.numbers.number_sets.real_numbers.nat_pos_within_real
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.nat1
^*equality replacement requirements