logo

Expression of type Forall

from the theory of proveit.logic.equality

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, c, f, fa, fx, x
from proveit.logic import Equals, Forall, Implies
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, x, a, c], instance_expr = Implies(Equals(x, a), Implies(Equals(fa, c), Equals(fx, c))))
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())
\forall_{f, x, a, c}~\left(\left(x = a\right) \Rightarrow \left(\left(f\left(a\right) = c\right) \Rightarrow \left(f\left(x\right) = c\right)\right)\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
with_wrappingIf 'True', wrap the Expression after the parametersNoneNone/False('with_wrapping',)
condition_wrappingWrap 'before' or 'after' the condition (or None).NoneNone/False('with_wrap_after_condition', 'with_wrap_before_condition')
wrap_paramsIf 'True', wraps every two parameters AND wraps the Expression after the parametersNoneNone/False('with_params',)
justificationjustify to the 'left', 'center', or 'right' in the array cellscentercenter('with_justification',)
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operand: 3
1Literal
2ExprTuple3
3Lambdaparameters: 4
body: 5
4ExprTuple21, 24, 23, 19
5Operationoperator: 10
operands: 6
6ExprTuple7, 8
7Operationoperator: 15
operands: 9
8Operationoperator: 10
operands: 11
9ExprTuple24, 23
10Literal
11ExprTuple12, 13
12Operationoperator: 15
operands: 14
13Operationoperator: 15
operands: 16
14ExprTuple17, 19
15Literal
16ExprTuple18, 19
17Operationoperator: 21
operand: 23
18Operationoperator: 21
operand: 24
19Variable
20ExprTuple23
21Variable
22ExprTuple24
23Variable
24Variable