Mizar source was "available upon request" for maybe 30-40 years. It got completely open-sourced under GPL some 3 years ago (maybe earlier, not sure), see [1], also [2] and [3] about an alternative implementation in Rust.
Mizar is indeed "scarcely advertised", but all the information is publicly available, who wants to know knows. As for Mizar semantics, see for example [4].
Yes, 50 years of LCF would have been much better. You should not talk about "50 years of proof assistants" and not mention Mizar which had the largest library of theorems for about half of that time.
Isabelle/HOL is still types. The underlying type theory of Isabelle/HOL is not theory of dependent types, but theory of simple types.
Isabelle/ZF would be a better example as it encodes Zermelo–Fraenkel set theory.
The example papers [1] [2] [3] [4] have 18 unique co-authors. Also, it's Beatriz.
> she makes analysis of several pairs of pictures
"We base our analysis on the catalog of 298,165 short-duration transients presented in Solano et al. (2022), detected in 200 red POSS-I plates with typical exposure times of 45–50 minutes." [1]
"Of the 2,718 days in this period, transients were observed on 310 days (11.4%)" [2]
"These searches significantly reduced the number of candidates (from 298 165 to 9 395)" [3]
> uniformly spread out across the whole plate
> thousands of uniformly spread out image defects
"we find a strong deficit of transient detections, at the 22 sigma statistical significance level, within the Earth’s umbral shadow" [1]
"we expect N = 1223 transients in shadow out of 106,339 total, corresponding to an expected fraction of fexp = 0.0115±0.00033. However, we observe only N = 349 transients in shadow" [1]
"Plate defects, by contrast, are expected to be randomly shaped and distributed" [1]
> in all pairs of plates the lights change one way only. On the first plate they are present and on the next plate 50 minutes later they disappear
"transients that appear only in one long exposure and are entirely absent shortly before and after" [1]
"In brief, transients were defined as distinct star-like point sources present in POSS-I E Red images that were absent both in images taken immediately prior to the POSS-I Red image and in all subsequent images." [2]
(*) POSS -- Palomar Observatory Sky Survey
[1] Aligned, multiple-transient events in the First Palomar Sky Survey, 2025, preprint
[2] Transients in the Palomar Observatory Sky Survey (POSS-I) may be associated with nuclear testing and reports of unidentified anomalous phenomena, Scientific Reports, 2025
[3] Discovering vanishing objects in POSS I red images using the Virtual Observatory, 2022, Monthly Notices of the Royal Astronomical Society, 515, 1380
[4] A glint in the eye: photographic plate archive searches for non-terrestrial artefacts, 2022, Acta Astronautica, 194, 106
Turns out looking for quotes directly contradicting debunker's statements is a great way to focus while reading a UAP-related scientific paper, thank you.
> except serve as a basis for practical formalization of proofs
I do formalized mathematics as a hobby and I can not see any basis for that opinion.
Freek Wiedijk wrote an interesting paper [0] where he compared the complexity of various foundations as encoded in Automath.
Mizar, which is based on Tarski–Grothendieck set theory (an extension of ZFC) is a proof assistant whose library was the largest for a couple of decades, only recently surpassed by Lean's Mathlib (perhaps). Metamath is mentioned below in comments and of course my favorite Isabelle/ZF are also based on ZFC.
[1] https://github.com/MizarProject/system [2] https://github.com/digama0/mizar-rs [3] https://arxiv.org/pdf/2304.08391v2 [4] https://link.springer.com/article/10.1007/s10817-018-9479-z