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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, b, f, fab, fxy, x, y
from proveit.logic import And, Equals, Forall, Implies
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [f, x, y, a, b], instance_expr = Implies(And(Equals(x, a), Equals(y, b)), Equals(fxy, fab)))
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, y, a, b}~\left(\left(\left(x = a\right) \land \left(y = b\right)\right) \Rightarrow \left(f\left(x, y\right) = f\left(a, b\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, 23, 24, 25, 26
5Operationoperator: 6
operands: 7
6Literal
7ExprTuple8, 9
8Operationoperator: 10
operands: 11
9Operationoperator: 18
operands: 12
10Literal
11ExprTuple13, 14
12ExprTuple15, 16
13Operationoperator: 18
operands: 17
14Operationoperator: 18
operands: 19
15Operationoperator: 21
operands: 20
16Operationoperator: 21
operands: 22
17ExprTuple23, 25
18Literal
19ExprTuple24, 26
20ExprTuple23, 24
21Variable
22ExprTuple25, 26
23Variable
24Variable
25Variable
26Variable