Expression of type ExprTuple

from the theory of proveit.core_expr_types.conditionals

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, ConditionalSet, ExprRange, ExprTuple, IndexedVar, Lambda, Variable, a, b, c, m, n
from proveit.core_expr_types import a_1_to_m, c_1_to_n
from proveit.logic import And, Equals, FALSE, Forall, InSet
from proveit.numbers import Natural, one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Lambda([m, n], Conditional(Forall(instance_param_or_params = [a_1_to_m, b, c_1_to_n], instance_expr = Equals(ConditionalSet(ExprRange(sub_expr1, Conditional(IndexedVar(a, sub_expr1), FALSE), one, m), b, ExprRange(sub_expr1, Conditional(IndexedVar(c, sub_expr1), FALSE), one, n)), b)), And(InSet(m, Natural), InSet(n, 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(m, n\right) \mapsto \left\{\forall_{a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}}~\left(\left\{\begin{array}{ccc}a_{1} \textrm{ if } \bot \\ a_{2} \textrm{ if } \bot \\  \vdots \\ a_{m} \textrm{ if } \bot \\ b \\ c_{1} \textrm{ if } \bot \\ c_{2} \textrm{ if } \bot \\  \vdots \\ c_{n} \textrm{ if } \bot\end{array}\right.. = b\right) \textrm{ if } m \in \mathbb{N} ,  n \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	32, 35
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	18, 29, 19
14	Operation	operator: 20 operands: 21
15	ExprTuple	32, 22
16	Literal
17	ExprTuple	35, 22
18	ExprRange	lambda_map: 23 start_index: 34 end_index: 32
19	ExprRange	lambda_map: 24 start_index: 34 end_index: 35
20	Literal
21	ExprTuple	25, 29
22	Literal
23	Lambda	parameter: 44 body: 38
24	Lambda	parameter: 44 body: 39
25	Operation	operator: 26 operands: 27
26	Literal
27	ExprTuple	28, 29, 30
28	ExprRange	lambda_map: 31 start_index: 34 end_index: 32
29	Variable
30	ExprRange	lambda_map: 33 start_index: 34 end_index: 35
31	Lambda	parameter: 44 body: 36
32	Variable
33	Lambda	parameter: 44 body: 37
34	Literal
35	Variable
36	Conditional	value: 38 condition: 40
37	Conditional	value: 39 condition: 40
38	IndexedVar	variable: 41 index: 44
39	IndexedVar	variable: 42 index: 44
40	Literal
41	Variable
42	Variable
43	ExprTuple	44
44	Variable