Expression of type Lambda

from the theory of proveit.core_expr_types.lambda_maps

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 Composition, Function, Lambda, f, fx, g, gy, gz, x, y, z
from proveit.logic import Equals

# build up the expression from sub-expressions
expr = Lambda([f, g], Equals(Composition(Lambda(x, fx), Lambda(y, gy)), Lambda(z, Function(f, [gz]))))

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())

\left(f, g\right) \mapsto \left(\left(\left[x \mapsto f\left(x\right)\right] \circ \left[y \mapsto g\left(y\right)\right]\right) = \left[z \mapsto f\left(g\left(z\right)\right)\right]\right)

stored_expr.style_options()

no style options

# display the expression information
stored_expr.expr_info()

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