Expression of type Lambda

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 Lambda, b, i
from proveit.core_expr_types import Len, a_1_to_i
from proveit.logic import Equals
from proveit.numbers import Add, one

# build up the expression from sub-expressions
sub_expr1 = [a_1_to_i, b]
expr = Lambda(sub_expr1, Equals(Len(operands = sub_expr1), Add(i, one)))

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_{i}, b\right) \mapsto \left(|\left(a_{1}, a_{2}, \ldots, a_{i}, b\right)| = \left(i + 1\right)\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameters: 7 body: 1
1	Operation	operator: 2 operands: 3
2	Literal
3	ExprTuple	4, 5
4	Operation	operator: 6 operands: 7
5	Operation	operator: 8 operands: 9
6	Literal
7	ExprTuple	10, 11
8	Literal
9	ExprTuple	14, 13
10	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
11	Variable
12	Lambda	parameter: 18 body: 15
13	Literal
14	Variable
15	IndexedVar	variable: 16 index: 18
16	Variable
17	ExprTuple	18
18	Variable