Expression of type Lambda

from the theory of proveit.physics.quantum.algebra

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, Conditional, Lambda, c
from proveit.logic import Forall, InClass, InSet
from proveit.numbers import Complex
from proveit.physics.quantum import Qmult, QmultCodomain

# build up the expression from sub-expressions
expr = Lambda(c, Conditional(Forall(instance_param_or_params = [A], instance_expr = InClass(Qmult(A, c), QmultCodomain), condition = InClass(Qmult(A), QmultCodomain)), InSet(c, Complex)))

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())

c \mapsto \left\{\forall_{A~|~\left[A\right] \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}}~\left(\left(A \thinspace c\right) \underset{{\scriptscriptstyle c}}{\in} \mathcal{Q^*}\right) \textrm{ if } c \in \mathbb{C}\right..

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Lambda	parameter: 23 body: 2
1	ExprTuple	23
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 9
4	Operation	operator: 7 operands: 8
5	Literal
6	ExprTuple	9
7	Literal
8	ExprTuple	23, 10
9	Lambda	parameter: 24 body: 11
10	Literal
11	Conditional	value: 12 condition: 13
12	Operation	operator: 15 operands: 14
13	Operation	operator: 15 operands: 16
14	ExprTuple	17, 19
15	Literal
16	ExprTuple	18, 19
17	Operation	operator: 21 operands: 20
18	Operation	operator: 21 operand: 24
19	Literal
20	ExprTuple	24, 23
21	Literal
22	ExprTuple	24
23	Variable
24	Variable