Expression of type Lambda

from the theory of proveit.logic.booleans.disjunction

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 B, Conditional, Lambda
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import Boolean, InSet, Or

# build up the expression from sub-expressions
expr = Lambda([A_1_to_m, B, C_1_to_n], Conditional(InSet(B, Boolean), InSet(Or(A_1_to_m, B, C_1_to_n), Boolean)))

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\{B \in \mathbb{B} \textrm{ if } \left(A_{1} \lor  A_{2} \lor  \ldots \lor  A_{m} \lor B\lor C_{1} \lor  C_{2} \lor  \ldots \lor  C_{n}\right) \in \mathbb{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: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 5 operands: 4
3	Operation	operator: 5 operands: 6
4	ExprTuple	12, 8
5	Literal
6	ExprTuple	7, 8
7	Operation	operator: 9 operands: 10
8	Literal
9	Literal
10	ExprTuple	11, 12, 13
11	ExprRange	lambda_map: 14 start_index: 17 end_index: 15
12	Variable
13	ExprRange	lambda_map: 16 start_index: 17 end_index: 18
14	Lambda	parameter: 24 body: 19
15	Variable
16	Lambda	parameter: 24 body: 20
17	Literal
18	Variable
19	IndexedVar	variable: 21 index: 24
20	IndexedVar	variable: 22 index: 24
21	Variable
22	Variable
23	ExprTuple	24
24	Variable