Expression of type Lambda

from the theory of proveit.core_expr_types.expr_arrays

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 A, B, ExprRange, IndexedVar, Lambda, Variable, k, n
from proveit.numbers import one

# build up the expression from sub-expressions
sub_expr1 = Variable("_b", latex_format = r"{_{-}b}")
sub_expr2 = Variable("_a", latex_format = r"{_{-}a}")
sub_expr3 = [sub_expr1, sub_expr2]
expr = Lambda(sub_expr1, [ExprRange(sub_expr2, IndexedVar(A, sub_expr3), one, n).with_explicit_parameterization(), ExprRange(sub_expr2, IndexedVar(B, sub_expr3), one, k)])

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())

{_{-}b} \mapsto \left(A_{{_{-}b}, 1}, A_{{_{-}b}, 2}, ..A_{{_{-}b}, {_{-}a}}.., A_{{_{-}b}, n},B_{{_{-}b}, 1}, B_{{_{-}b}, 2}, \ldots, B_{{_{-}b}, k}\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 16 body: 2
1	ExprTuple	16
2	ExprTuple	3, 4
3	ExprRange	lambda_map: 5 start_index: 8 end_index: 6
4	ExprRange	lambda_map: 7 start_index: 8 end_index: 9
5	Lambda	parameter: 17 body: 10
6	Variable
7	Lambda	parameter: 17 body: 12
8	Literal
9	Variable
10	IndexedVar	variable: 13 indices: 15
11	ExprTuple	17
12	IndexedVar	variable: 14 indices: 15
13	Variable
14	Variable
15	ExprTuple	16, 17
16	Variable
17	Variable