Expression of type Lambda

from the theory of proveit.logic.booleans.quantification.existence

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, alpha
from proveit.core_expr_types import P__x_1_to_n, Q__x_1_to_n, x_1_to_n
from proveit.logic import Implies

# build up the expression from sub-expressions
expr = Lambda([x_1_to_n], Conditional(Implies(P__x_1_to_n, alpha), Q__x_1_to_n))

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(x_{1}, x_{2}, \ldots, x_{n}\right) \mapsto \left\{P\left(x_{1}, x_{2}, \ldots, x_{n}\right) \Rightarrow \alpha \textrm{ if } Q\left(x_{1}, x_{2}, \ldots, x_{n}\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: 10 body: 1
1	Conditional	value: 2 condition: 3
2	Operation	operator: 4 operands: 5
3	Operation	operator: 6 operands: 10
4	Literal
5	ExprTuple	7, 8
6	Variable
7	Operation	operator: 9 operands: 10
8	Variable
9	Variable
10	ExprTuple	11
11	ExprRange	lambda_map: 12 start_index: 13 end_index: 14
12	Lambda	parameter: 18 body: 15
13	Literal
14	Variable
15	IndexedVar	variable: 16 index: 18
16	Variable
17	ExprTuple	18
18	Variable