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