Expression of type Lambda

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, 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 Equals, FALSE
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = Lambda([a_1_to_m, b, c_1_to_n], 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))

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(a_{1}, a_{2}, \ldots, a_{m}, b, c_{1}, c_{2}, \ldots, c_{n}\right) \mapsto \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)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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