Expression of type ExprTuple

from the theory of proveit.core_expr_types.tuples

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, b, d, i, k
from proveit.core_expr_types import a_1_to_i, c_1_to_k
from proveit.logic import And, Equals, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
expr = ExprTuple(Lambda([i, k], Conditional(Forall(instance_param_or_params = [a_1_to_i, b, c_1_to_k, d], instance_expr = Equals([a_1_to_i, b, c_1_to_k], [a_1_to_i, d, c_1_to_k]).with_wrapping_at(2), condition = Equals(b, d)), And(InSet(i, Natural), InSet(k, Natural)))))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(\left(i, k\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{i}, b, c_{1}, c_{2}, \ldots, c_{k}, d~|~b = d}~\left(\begin{array}{c} \begin{array}{l} \left(a_{1}, a_{2}, \ldots, a_{i}, b,c_{1}, c_{2}, \ldots, c_{k}\right) =  \\ \left(a_{1}, a_{2}, \ldots, a_{i}, d,c_{1}, c_{2}, \ldots, c_{k}\right) \end{array} \end{array}\right) \textrm{ if } i \in \mathbb{N} ,  k \in \mathbb{N}\right..\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1
1	Lambda	parameters: 2 body: 3
2	ExprTuple	31, 34
3	Conditional	value: 4 condition: 5
4	Operation	operator: 6 operand: 10
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10
8	Literal
9	ExprTuple	11, 12
10	Lambda	parameters: 13 body: 14
11	Operation	operator: 16 operands: 15
12	Operation	operator: 16 operands: 17
13	ExprTuple	27, 26, 29, 28
14	Conditional	value: 18 condition: 19
15	ExprTuple	31, 20
16	Literal
17	ExprTuple	34, 20
18	Operation	operator: 22 operands: 21
19	Operation	operator: 22 operands: 23
20	Literal
21	ExprTuple	24, 25
22	Literal
23	ExprTuple	26, 28
24	ExprTuple	27, 26, 29
25	ExprTuple	27, 28, 29
26	Variable
27	ExprRange	lambda_map: 30 start_index: 33 end_index: 31
28	Variable
29	ExprRange	lambda_map: 32 start_index: 33 end_index: 34
30	Lambda	parameter: 40 body: 35
31	Variable
32	Lambda	parameter: 40 body: 36
33	Literal
34	Variable
35	IndexedVar	variable: 37 index: 40
36	IndexedVar	variable: 38 index: 40
37	Variable
38	Variable
39	ExprTuple	40
40	Variable