Expression of type Lambda

from the theory of proveit.logic.sets.functions.injections

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, C, Conditional, Lambda, f
from proveit.logic import InSet, Injections

# build up the expression from sub-expressions
expr = Lambda(f, Conditional(InSet(f, Injections(A, C)), InSet(f, Injections(B, C))))

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())

f \mapsto \left\{f \in \left[A \xrightarrow[]{\text{1-to-1}} C\right] \textrm{ if } f \in \left[B \xrightarrow[]{\text{1-to-1}} C\right]\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 9 body: 2
1	ExprTuple	9
2	Conditional	value: 3 condition: 4
3	Operation	operator: 6 operands: 5
4	Operation	operator: 6 operands: 7
5	ExprTuple	9, 8
6	Literal
7	ExprTuple	9, 10
8	Operation	operator: 12 operands: 11
9	Variable
10	Operation	operator: 12 operands: 13
11	ExprTuple	14, 16
12	Literal
13	ExprTuple	15, 16
14	Variable
15	Variable
16	Variable