3.3.4 and 3.3.5

Makefile

@@ -2,7 +2,6 @@ GENDIR := html/src/generated
 AGDA_SOURCES := $(shell find src -not \( -path src/Misc -prune \) \( -name "*.agda" -o -name "*.lagda.md" \) )
 
 build-to-html:
-	nu scripts/build-table
 	find src \
 		-not \( -path src/Misc -prune \) \
 		\( -name "*.agda" -o -name "*.lagda.md" \) \
@@ -14,7 +13,7 @@ build-to-html:
 		--html-highlight=auto \
 		--no-load-primitives \
 		|| true
-	fd --no-ignore "html$$" $(GENDIR) -x rm
+	# fd --no-ignore "html$$" $(GENDIR) -x rm
 
 .PHONY: html/src/generated/Progress.md
 
@@ -25,8 +24,8 @@ html/book/Progress.html: html/src/generated/Progress.md
 	pandoc \
 		-f markdown-markdown_in_html_blocks+raw_html \
 		-t html \
-		-i html/src/generated/Progress.md \
+		-i $^ \
-		> html/book/Progress.html
+		> $@
 	
 html/book/progress/index.html: html/book/Progress.html
 	cat html/ProgressHeader.html $^ > $@
@@ -38,7 +37,7 @@ build-book: build-to-html
 refresh-book: build-to-html
 	mdbook serve html
 
-deploy: build-book html/book/Progress.html
+deploy: build-book html/book/progress/index.html
 	rsync -azr html/book/ root@veil:/home/blogDeploy/public/research
 
 .PHONY: build-book build-to-html deploy

scripts/build-table

@@ -83,8 +83,6 @@ let vizChapter = { |n|
     | each { $in | update column1 { do $viz ($in | where completed == "x" | length) ($in | length) } }
     | sort-by -n column0
 
-  print ($table2 | table)
-
   let newColumn1 = { column0: "Ch", column1: (do $vizCh $n $table) }
   let newColumn2 = { column0: "Chnum", column1: $n }
 

src/HottBook/Chapter2.lagda.md

@@ -784,7 +784,7 @@ open axiom2∙10∙3
 --   ap f , qinv-to-isequiv eqv
 ```
 
-### Theorem 2.11.2
+### Lemma 2.11.2
 
 ```
 module lemma2∙11∙2 where

src/HottBook/Chapter3.lagda.md

@@ -270,6 +270,47 @@ lemma3∙3∙2 {P} pp x0 =
 
 {{#include HottBook.Chapter3Lemma333.md:lemma333}}
 
+### Lemma 3.3.4
+
+```
+lemma3∙3∙4 : {A : Set} → isProp A → isSet A
+lemma3∙3∙4 {A} f x y p q =
+  let
+    g : (y : A) → x ≡ y
+    g y = f x y
+
+    step : (y z : A) → (p : y ≡ z) → transport (λ w → x ≡ w) p (g y) ≡ g z
+    step y z p = apd g p
+
+    step2 : (y z : A) → (p : y ≡ z) → (g y) ∙ p ≡ g z
+    step2 y z p = sym (lemma2∙11∙2.i p (g y)) ∙ step y z p
+
+    step3 : (y z : A) → (p : y ≡ z) → p ≡ sym (g y) ∙ (g z)
+    step3 y z p =
+      lemma2∙1∙4.i2 p
+      ∙ ap (λ q → q ∙ p) (sym (lemma2∙1∙4.ii1 (g y)))
+      ∙ sym (lemma2∙1∙4.iv (sym (g y)) (g y) p)
+      ∙ ap (λ q → sym (g y) ∙ q) (step2 y z p)
+
+    step4 = step3 x y p
+    step5 = step3 x y q
+  in step4 ∙ sym step5
+```
+
+### Lemma 3.3.5
+
+```
+module lemma3∙3∙5 where
+  open axiom2∙9∙3
+
+  i : {A : Set} → isProp (isProp (A))
+  i f g = funext λ x → funext λ y → (lemma3∙3∙4 f) x y (f x y) (g x y)
+
+  ii : {A : Set} → isProp (isSet (A))
+  ii f g = funext λ x → funext λ y → funext λ p → funext λ q →
+    (lemma3∙1∙8 f) x y p q (f x y p q) (g x y p q)
+```
+
 ## 3.4 Classical vs. intuitionistic logic
 
 ### Definition 3.4.3
@@ -409,6 +450,18 @@ lemma3∙9∙1 {P} Pprop = lemma3∙3∙3 Pprop prop2 ∣_∣ g
           admit : x ≡ y
 ```
 
+### Corollary 3.9.2
+
+Principle of unique choice
+
+```
+-- corollary3∙9∙2 : {A : Set} {P : A → Set}
+--   → ((x : A) → isProp (P x))
+--   → ((x : A) → ∥ P x ∥)
+--   → (x : A) → P x
+-- corollary3∙9∙2 assump1 assump2 x = {!   !}
+```
+
 ## 3.11 Contractibility
 
 ### Definition 3.11.1
@@ -565,3 +618,14 @@ module lemma3∙11∙9 where
           y : (q : a ≡ x) → transport P q (transport P (sym q) p) ≡ p
           y refl = refl
 ```
+
+### Lemma 3.11.10
+
+```
+module lemma3∙11∙10 where
+  i : {A : Set} → ((x y : A) → isContr (x ≡ y)) → isProp A
+  i f x y = Σ.fst (f x y)
+
+  ii : {A : Set} → isProp A → ((x y : A) → isContr (x ≡ y))
+  ii f x y = f x y , λ z → {!   !}
+```