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, Lambda, a
from proveit.core_expr_types import Q_1_to_m, R_1_to_n
from proveit.logic import And, Equals

# build up the expression from sub-expressions
expr = Lambda([a, Q_1_to_m, R_1_to_n], Equals(Conditional(a, And(And(Q_1_to_m), And(R_1_to_n))), Conditional(a, And(Q_1_to_m, R_1_to_n))).with_wrapping_at(1))

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, Q_{1}, Q_{2}, \ldots, Q_{m}, R_{1}, R_{2}, \ldots, R_{n}\right) \mapsto \left(\begin{array}{c} \begin{array}{l} \left\{a \textrm{ if } Q_{1} \land  Q_{2} \land  \ldots \land  Q_{m} ,  R_{1} \land  R_{2} \land  \ldots \land  R_{n}\right.. \\  = \left\{a \textrm{ if } Q_{1} ,  Q_{2} ,  \ldots ,  Q_{m}, R_{1} ,  R_{2} ,  \ldots ,  R_{n}\right.. \end{array} \end{array}\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	8, 17, 18
2	Operation	operator: 3 operands: 4
3	Literal
4	ExprTuple	5, 6
5	Conditional	value: 8 condition: 7
6	Conditional	value: 8 condition: 9
7	Operation	operator: 15 operands: 10
8	Variable
9	Operation	operator: 15 operands: 11
10	ExprTuple	12, 13
11	ExprTuple	17, 18
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17
15	Literal
16	ExprTuple	18
17	ExprRange	lambda_map: 19 start_index: 22 end_index: 20
18	ExprRange	lambda_map: 21 start_index: 22 end_index: 23
19	Lambda	parameter: 29 body: 24
20	Variable
21	Lambda	parameter: 29 body: 25
22	Literal
23	Variable
24	IndexedVar	variable: 26 index: 29
25	IndexedVar	variable: 27 index: 29
26	Variable
27	Variable
28	ExprTuple	29
29	Variable