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Expression of type Forall

from the theory of proveit.linear_algebra.scalar_multiplication

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 K, V, alpha, beta, x
from proveit.linear_algebra import ScalarMult, VecSpaces
from proveit.logic import Equals, Forall
In [2]:
# build up the expression from sub-expressions
expr = Forall(instance_param_or_params = [K], instance_expr = Forall(instance_param_or_params = [V], instance_expr = Forall(instance_param_or_params = [x], instance_expr = Forall(instance_param_or_params = [alpha, beta], instance_expr = Equals(ScalarMult(alpha, ScalarMult(beta, x)), ScalarMult(ScalarMult(alpha, beta), x)), domain = K), domain = V), domain = VecSpaces(K)))
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_{K}~\left[\forall_{V \underset{{\scriptscriptstyle c}}{\in} \textrm{VecSpaces}\left(K\right)}~\left[\forall_{x \in V}~\left[\forall_{\alpha, \beta \in K}~\left(\left(\alpha \cdot \left(\beta \cdot x\right)\right) = \left(\left(\alpha \cdot \beta\right) \cdot x\right)\right)\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: 21
operand: 2
1ExprTuple2
2Lambdaparameter: 44
body: 3
3Operationoperator: 21
operand: 5
4ExprTuple5
5Lambdaparameter: 25
body: 7
6ExprTuple25
7Conditionalvalue: 8
condition: 9
8Operationoperator: 21
operand: 13
9Operationoperator: 11
operands: 12
10ExprTuple13
11Literal
12ExprTuple25, 14
13Lambdaparameter: 48
body: 16
14Operationoperator: 17
operand: 44
15ExprTuple48
16Conditionalvalue: 19
condition: 20
17Literal
18ExprTuple44
19Operationoperator: 21
operand: 24
20Operationoperator: 40
operands: 23
21Literal
22ExprTuple24
23ExprTuple48, 25
24Lambdaparameters: 47
body: 26
25Variable
26Conditionalvalue: 27
condition: 28
27Operationoperator: 29
operands: 30
28Operationoperator: 31
operands: 32
29Literal
30ExprTuple33, 34
31Literal
32ExprTuple35, 36
33Operationoperator: 46
operands: 37
34Operationoperator: 46
operands: 38
35Operationoperator: 40
operands: 39
36Operationoperator: 40
operands: 41
37ExprTuple49, 42
38ExprTuple43, 48
39ExprTuple49, 44
40Literal
41ExprTuple50, 44
42Operationoperator: 46
operands: 45
43Operationoperator: 46
operands: 47
44Variable
45ExprTuple50, 48
46Literal
47ExprTuple49, 50
48Variable
49Variable
50Variable