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Expression of type Conditional

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

In [1]:
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, Conditional, a, b, f, fa, fb
from proveit.logic import And, Forall, Functions, InSet, Injections, NotEquals
In [2]:
# build up the expression from sub-expressions
expr = Conditional(And(InSet(f, Functions(A, B)), Forall(instance_param_or_params = [a, b], instance_expr = NotEquals(fa, fb), domain = A, condition = NotEquals(a, b))), InSet(f, Injections(A, B)))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left\{\left(f \in \left[A \rightarrow B\right]\right) \land \left[\forall_{a, b \in A~|~a \neq b}~\left(f\left(a\right) \neq f\left(b\right)\right)\right] \textrm{ if } f \in \left[A \xrightarrow[]{\text{1-to-1}} B\right]\right..
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
condition_delimiter'comma' or 'and'commacomma('with_comma_delimiter', 'with_conjunction_delimiter')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Conditionalvalue: 1
condition: 2
1Operationoperator: 21
operands: 3
2Operationoperator: 32
operands: 4
3ExprTuple5, 6
4ExprTuple29, 7
5Operationoperator: 32
operands: 8
6Operationoperator: 9
operand: 13
7Operationoperator: 11
operands: 15
8ExprTuple29, 12
9Literal
10ExprTuple13
11Literal
12Operationoperator: 14
operands: 15
13Lambdaparameters: 35
body: 16
14Literal
15ExprTuple36, 17
16Conditionalvalue: 18
condition: 19
17Variable
18Operationoperator: 34
operands: 20
19Operationoperator: 21
operands: 22
20ExprTuple23, 24
21Literal
22ExprTuple25, 26, 27
23Operationoperator: 29
operand: 37
24Operationoperator: 29
operand: 38
25Operationoperator: 32
operands: 31
26Operationoperator: 32
operands: 33
27Operationoperator: 34
operands: 35
28ExprTuple37
29Variable
30ExprTuple38
31ExprTuple37, 36
32Literal
33ExprTuple38, 36
34Literal
35ExprTuple37, 38
36Variable
37Variable
38Variable