Meaning of U+22B6 and possible mistakes

[Ivan Panchenko]

Consider the following character names:

ORIGINAL OF (⊶, U+22B6)
IMAGE OF (⊷, U+22B7)

I find “original” as a noun strange in this context. How about “origin”,
“domain” or “source”? However, the only mathematical use of “⊶” that I
found was in the context of zooms as defined in section 1.5 here:
https://arxiv.org/pdf/0706.1033.pdf

This work is from 2010, but the character already existed in Unicode 1.0.0,
so I am not sure what it was supposed to mean after all. Any hint? Perhaps
U+2290 ⊐ SQUARE ORIGINAL OF was supposed to have the same meaning as U+22B6
(why else would it be named this way?).

Furthermore:

SUBSET OF WITH NOT EQUAL TO (⊊, U+228A)
LESS-THAN BUT NOT EQUAL TO (≨, U+2268)
SQUARE ORIGINAL OF OR NOT EQUAL TO (⋥, U+22E5)

The first of these names employs the word “with” to describe how U+228A
looks like, the second one employs the word “but” to describe what U+2268
means. (A bit inconsistent, but fine so far.)

In the third one, I find the “or not equal to” part strange. Would “BUT not
equal to” not be more plausible?

Sidenote (not an issue with Unicode): I find it remarkable that while “≤”
is used to mean ‘is less than OR equal to’, we use “⊊” for ‘is a subset of
AND not equal to’, which breaks the analogy. I might prefer “⊊︀” (with
stroke through bottom members) to “⊊” for this reason. The file bsymbols.mf
of amsfonts deviously contains “cmchar "Subset or not equal to sign"”. Cf.
Paul Taylor for a criticism of the use of “⊂” for the proper subset
relation:
https://books.google.com/books?id=iSCqyNgzamcC&pg=PA75&q=%22but+strict+inclusion+is+neither+primitive%22
Schröder (1890) actually used a symbol (in the strict sense) that looked
similar to our “⊂” but went up- and downwards like the less-than sign; I do
not advocate reintroducing it either since we also write “∩” and “∪”
(analogously to “∧” and “∨”) with parallel lines.
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