Logiweb sequent calculus, Chores

Klaus Grue

26. juni 2006

Indhold

1 Test cases 1

2 Pyk definitions 1

3 TEX definitions 5 3.1 Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4 Numerals 13

5 Priority table 14

1 Test cases

2 Pyk definitions

[\overline{0} →^{pyk} “numeral zero”] [\overline{1} →^{pyk} “numeral one”] [\overline{2} →^{pyk} “numeral two”] [\overline{3} →^{pyk} “numeral three”] [\overline{4} →^{pyk} “numeral four”] [\overline{5} →^{pyk} “numeral five”] [\overline{6} →^{pyk} “numeral six”] [\overline{7} →^{pyk} “numeral seven”] [\overline{8} →^{pyk} “numeral eight”] [\overline{9} →^{pyk} “numeral nine”] [rule div →^{pyk} “rule div”] [R →^{pyk} “rule r”] [R1 →^{pyk} “rule r one”] [R2 →^{pyk} “rule r two”] [R3 →^{pyk} “rule r three”] [R4 →^{pyk} “rule r four”] [R5 →^{pyk} “rule r five”] [R6 →^{pyk} “rule r six”] [Con1 →^{pyk} “conjel1”] [Con2 →^{pyk} “conjel2”] [Con →^{pyk} “conjin”] [Dis1 →^{pyk} “disjin1”] [Dis2 →^{pyk} “disjin2”] [T1 →^{pyk} “t one”] [T0 →^{pyk} “t zero”] [H0a →^{pyk} “h zero a”] [H0b →^{pyk} “h zero b”] [H1 →^{pyk} “h one”] [H2 →^{pyk} “h two”] [S10 →^{pyk} “axiom s ten”] [Prop 3.2 →^{pyk} “prop three two”] [Prop 3.2i →^{pyk} “prop three two i”] [Prop 3.2j_{1} →^{pyk} “prop three two j one”] [Prop 3.2j_{2} →^{pyk} “prop three two j two”] [Prop 3.2j →^{pyk} “prop three two j”] [Prop 3.2k_{1} →^{pyk} “prop three two k one”] [Prop 3.2k_{2} →^{pyk} “prop three two k two”] [Prop 3.2k →^{pyk} “prop three two k”] [Prop 3.2l_{1} →^{pyk} “prop three two l one”] [Prop 3.2l_{2} →^{pyk} “prop three two l two”] [Prop 3.2l →^{pyk} “prop three two l”] [Prop 3.2m_{1} →^{pyk} “prop three two m one”] [Prop 3.2m_{2} →^{pyk} “prop three two m two”] [Prop 3.2m →^{pyk} “prop three two m”] [Prop 3.2n_{1} →^{pyk} “prop three two n one”] [Prop 3.2n_{2} →^{pyk} “prop three two n two”] [Prop 3.2n →^{pyk} “prop three two n”] [Prop 3.2o →^{pyk} “prop three two o”] [Prop 3.4 →^{pyk} “prop three four”] [Prop 3.4a_{1} →^{pyk} “prop three four a one”] [Prop 3.4a_{2} →^{pyk} “prop three four a two”] [Prop 3.4a →^{pyk} “prop three four a”] [Prop 3.4b →^{pyk} “prop three four b”] [Prop 3.4c_{1} →^{pyk} “prop three four c one”] [Prop 3.4c_{2} →^{pyk} “prop three four c two”] [Prop 3.4c →^{pyk} “prop three four c”] [Prop 3.4d_{1} →^{pyk} “prop three four d one”] [Prop 3.4d_{2} →^{pyk} “prop three four d two”] [Prop 3.4d →^{pyk} “prop three four d”] [Prop 3.5 →^{pyk} “prop three five”] [Prop 3.5a →^{pyk} “prop three five a”] [Prop 3.5b →^{pyk} “prop three five b”] [Prop 3.5c →^{pyk} “prop three five c”] [Prop 3.5d_{1} →^{pyk} “prop three five d one”] [Prop 3.5d_{2} →^{pyk} “prop three five d two”] [Prop 3.5d →^{pyk} “prop three five d”] [Prop 3.5e_{1} →^{pyk} “prop three five e one”] [Prop 3.5e_{2} →^{pyk} “prop three five e two”] [Prop 3.5e →^{pyk} “prop three five e”] [Prop 3.5f_{1} →^{pyk} “prop three five f one”] [Prop 3.5f_{2} →^{pyk} “prop three five f two”] [Prop 3.5f →^{pyk} “prop three five f”] [Prop 3.5g_{1} →^{pyk} “prop three five g one”] [Prop 3.5g_{2} →^{pyk} “prop three five g two”] [Prop 3.5g →^{pyk} “prop three five g”] [Prop 3.5h_{1} →^{pyk} “prop three five h one”] [Prop 3.5h_{2} →^{pyk} “prop three five h two”] [Prop 3.5h →^{pyk} “prop three five h”] [Prop 3.5i_{1} →^{pyk} “prop three five i one”] [Prop 3.5i_{2} →^{pyk} “prop three five i two”] [Prop 3.5i →^{pyk} “prop three five i”] [Prop 3.5j_{1} →^{pyk} “prop three five j one”] [Prop 3.5j_{2} →^{pyk} “prop three five j two”] [Prop 3.5j →^{pyk} “prop three five j”] [Prop 3.7 →^{pyk} “prop three seven”] [Prop 3.7a →^{pyk} “prop three seven a”] [Prop 3.7b →^{pyk} “prop three seven b”] [Prop 3.7c →^{pyk} “prop three seven c”] [Prop 3.7d →^{pyk} “prop three seven d”] [Prop 3.7e →^{pyk} “prop three seven e”] [Prop 3.7f →^{pyk} “prop three seven f”] [Prop 3.7g →^{pyk} “prop three seven g”] [Prop 3.7g′ →^{pyk} “prop three seven g mark”] [Prop 3.7h →^{pyk} “prop three seven h”] [Prop 3.7i →^{pyk} “prop three seven i”] [Prop 3.7j →^{pyk} “prop three seven j”] [Prop 3.7k →^{pyk} “prop three seven k”] [Prop 3.7k′ →^{pyk} “prop three seven k mark”] [Prop 3.7l →^{pyk} “prop three seven l”] [Prop 3.7l′ →^{pyk} “prop three seven l mark”] [Prop 3.7m →^{pyk} “prop three seven m”] [Prop 3.7n →^{pyk} “prop three seven n”] [Prop 3.7o →^{pyk} “prop three seven o”] [Prop 3.7p →^{pyk} “prop three seven p”] [Prop 3.7q →^{pyk} “prop three seven q”] [Prop 3.7r →^{pyk} “prop three seven r”] [Prop 3.7s →^{pyk} “prop three seven s”] [Prop 3.7t →^{pyk} “prop three seven t”] [Prop 3.7u →^{pyk} “prop three seven u”] [Prop 3.7u′ →^{pyk} “prop three seven u mark”] [Prop 3.7v →^{pyk} “prop three seven v”] [Prop 3.7w →^{pyk} “prop three seven w”] [Prop 3.7x →^{pyk} “prop three seven x”] [Prop 3.7x′ →^{pyk} “prop three seven x mark”] [Prop 3.7y →^{pyk} “prop three seven y”] [Prop 3.7y′ →^{pyk} “prop three seven y mark”] [Prop 3.7z →^{pyk} “prop three seven z”] [Prop 3.7z′ →^{pyk} “prop three seven z mark”] [Prop 3.10 →^{pyk} “prop three ten”] [Prop 3.10a →^{pyk} “prop three ten a”] [Prop 3.10b →^{pyk} “prop three ten b”] [Prop 3.10c →^{pyk} “prop three ten c”] [Prop 3.10d →^{pyk} “prop three ten d”] [Prop 3.10e →^{pyk} “prop three ten e”] [Prop 3.10f →^{pyk} “prop three ten f”] [Prop 3.10g →^{pyk} “prop three ten g”] [Prop 3.10h →^{pyk} “prop three ten h”] [Prop 3.11 →^{pyk} “prop three eleven”]

[∗ < ∗ →^{pyk} “" ist "”]

[∗ ≤ ∗ →^{pyk} “" istq "”]

[∗ ≮ ∗ →^{pyk} “" inst "”]

[∗ > ∗ →^{pyk} “" igt "”]

[∗ ≥ ∗ →^{pyk} “" igtq "”]

[∗ ≯ ∗ →^{pyk} “" ingt "”]

[∗ ≠ ∗ →^{pyk} “" neq "”]

[∗ ∧ ∗ →^{pyk} “" and1 "”]

[∗ ∨ ∗ →^{pyk} “" or1 "”]

[∃∗: ∗ →^{pyk} “exists " indeed "”] [∗ | ∗ →^{pyk} “" divides "”] [∗ … →^{pyk} “" ldots”] [frozen →^{pyk} “frozen”]

3 TEX definitions

[∃x: y →^{tex} “

\exists #1.
\colon #2.”]

[S10 →^{tex} “

S10”]

[x | y →^{tex} “#1.

\mathrel{|} #2.”]

[Prop 3.2 →^{tex} “

Prop\ 3.2”] [Prop 3.2i →^{tex} “

Prop\ 3.2i”]

[Prop 3.2j →^{tex} “ Prop\ 3.2j”]

[Prop 3.2j_{1} →^{tex} “ Prop\ 3.2j 1”]

[Prop 3.2j_{2} →^{tex} “ Prop\ 3.2j 2”]

[Prop 3.2k →^{tex} “ Prop\ 3.2k”]

[Prop 3.2k_{1} →^{tex} “ Prop\ 3.2k 1”]

[Prop 3.2k_{2} →^{tex} “ Prop\ 3.2k 2”]

[Prop 3.2l →^{tex} “ Prop\ 3.2l”]

[Prop 3.2l_{1} →^{tex} “ Prop\ 3.2l 1”]

[Prop 3.2l_{2} →^{tex} “ Prop\ 3.2l 2”]

[Prop 3.2m →^{tex} “ Prop\ 3.2m”]

[Prop 3.2m_{1} →^{tex} “ Prop\ 3.2m 1”]

[Prop 3.2m_{2} →^{tex} “ Prop\ 3.2m 2”]

[Prop 3.2n →^{tex} “ Prop\ 3.2n”]

[Prop 3.2n_{1} →^{tex} “ Prop\ 3.2n 1”]

[Prop 3.2n_{2} →^{tex} “ Prop\ 3.2n 2”] [Prop 3.2o →^{tex} “

Prop\ 3.2o”]

[Prop 3.4 →^{tex} “

Prop\ 3.4”]

[Prop 3.4a_{1} →^{tex} “ Prop\ 3.4a 1”]

[Prop 3.4a_{2} →^{tex} “ Prop\ 3.4a 2”]

[Prop 3.4a →^{tex} “ Prop\ 3.4a”]

[Prop 3.4b →^{tex} “ Prop\ 3.4b”]

[Prop 3.4c_{1} →^{tex} “ Prop\ 3.4c 1”]

[Prop 3.4c_{2} →^{tex} “ Prop\ 3.4c 2”]

[Prop 3.4c →^{tex} “ Prop\ 3.4c”]

[Prop 3.4d_{1} →^{tex} “ Prop\ 3.4d 1”]

[Prop 3.4d_{2} →^{tex} “ Prop\ 3.4d 2”]

[Prop 3.4d →^{tex} “ Prop\ 3.4d”]

[Prop 3.5 →^{tex} “

Prop\ 3.5”]

[Prop 3.5a →^{tex} “ Prop\ 3.5a”]

[Prop 3.5b →^{tex} “ Prop\ 3.5b”]

[Prop 3.5c →^{tex} “ Prop\ 3.5c”] [Prop 3.5d_{1} →^{tex} “

Prop\ 3.5d 1”]

[Prop 3.5d_{2} →^{tex} “ Prop\ 3.5d 2”]

[Prop 3.5d →^{tex} “ Prop\ 3.5d”]

[Prop 3.5e_{1} →^{tex} “ Prop\ 3.5e 1”]

[Prop 3.5e_{2} →^{tex} “ Prop\ 3.5e 2”]

[Prop 3.5e →^{tex} “ Prop\ 3.5e”]

[Prop 3.5f_{1} →^{tex} “ Prop\ 3.5f 1”]

[Prop 3.5f_{2} →^{tex} “ Prop\ 3.5f 2”]

[Prop 3.5f →^{tex} “ Prop\ 3.5f”]

[Prop 3.5g_{1} →^{tex} “ Prop\ 3.5g 1”]

[Prop 3.5g_{2} →^{tex} “ Prop\ 3.5g 2”]

[Prop 3.5g →^{tex} “ Prop\ 3.5g”]

[Prop 3.5h_{1} →^{tex} “ Prop\ 3.5h 1”]

[Prop 3.5h_{2} →^{tex} “ Prop\ 3.5h 2”]

[Prop 3.5h →^{tex} “ Prop\ 3.5h”]

[Prop 3.5i_{1} →^{tex} “ Prop\ 3.5i 1”] [Prop 3.5i_{2} →^{tex} “

Prop\ 3.5i 2”]

[Prop 3.5i →^{tex} “ Prop\ 3.5i”]

[Prop 3.5j_{1} →^{tex} “ Prop\ 3.5j 1”]

[Prop 3.5j_{2} →^{tex} “ Prop\ 3.5j 2”]

[Prop 3.5j →^{tex} “ Prop\ 3.5j”]

[Prop 3.7 →^{tex} “

Prop\ 3.7”]

[Prop 3.7a →^{tex} “ Prop\ 3.7a”]

[Prop 3.7b →^{tex} “ Prop\ 3.7b”]

[Prop 3.7c →^{tex} “ Prop\ 3.7c”]

[Prop 3.7d →^{tex} “ Prop\ 3.7d”]

[Prop 3.7e →^{tex} “ Prop\ 3.7e”]

[Prop 3.7f →^{tex} “ Prop\ 3.7f”]

[Prop 3.7g →^{tex} “ Prop\ 3.7g”]

[Prop 3.7g′ →^{tex} “ Prop\ 3.7g’”]

[Prop 3.7h →^{tex} “ Prop\ 3.7h”]

[Prop 3.7i →^{tex} “ Prop\ 3.7i”] [Prop 3.7j →^{tex} “

Prop\ 3.7j”]

[Prop 3.7k →^{tex} “ Prop\ 3.7k”]

[Prop 3.7k′ →^{tex} “ Prop\ 3.7k’”]

[Prop 3.7l →^{tex} “ Prop\ 3.7l”]

[Prop 3.7l′ →^{tex} “ Prop\ 3.7l’”]

[Prop 3.7m →^{tex} “ Prop\ 3.7m”]

[Prop 3.7n →^{tex} “ Prop\ 3.7n”]

[Prop 3.7o →^{tex} “ Prop\ 3.7o”]

[Prop 3.7p →^{tex} “ Prop\ 3.7p”]

[Prop 3.7q →^{tex} “ Prop\ 3.7q”]

[Prop 3.7r →^{tex} “ Prop\ 3.7r”]

[Prop 3.7s →^{tex} “ Prop\ 3.7s”]

[Prop 3.7t →^{tex} “ Prop\ 3.7t”]

[Prop 3.7u →^{tex} “ Prop\ 3.7u”]

[Prop 3.7u′ →^{tex} “ Prop\ 3.7u’”]

[Prop 3.7v →^{tex} “ Prop\ 3.7v”] [Prop 3.7w →^{tex} “

Prop\ 3.7w”]

[Prop 3.7x →^{tex} “ Prop\ 3.7x”]

[Prop 3.7x′ →^{tex} “ Prop\ 3.7x’”]

[Prop 3.7y →^{tex} “ Prop\ 3.7y”]

[Prop 3.7y′ →^{tex} “ Prop\ 3.7y’”]

[Prop 3.7z →^{tex} “ Prop\ 3.7z”]

[Prop 3.7z′ →^{tex} “ Prop\ 3.7z’”]

[Prop 3.10 →^{tex} “

Prop\ 3.10”]

[Prop 3.10a →^{tex} “ Prop\ 3.10a”]

[Prop 3.10b →^{tex} “ Prop\ 3.10b”]

[Prop 3.10c →^{tex} “ Prop\ 3.10c”]

[Prop 3.10d →^{tex} “ Prop\ 3.10d”]

[Prop 3.10e →^{tex} “ Prop\ 3.10e”]

[Prop 3.10f →^{tex} “ Prop\ 3.10f”]

[Prop 3.10g →^{tex} “ Prop\ 3.10g”]

[Prop 3.10h →^{tex} “ Prop\ 3.10h”]

[Prop 3.11 →^{tex} “

Prop\ 3.11”]

[R →^{tex} “

R”]

[R1 →^{tex} “

R1”]

[R2 →^{tex} “

R2”]

[R3 →^{tex} “

R3”]

[R4 →^{tex} “

R4”]

[R5 →^{tex} “

R5”]

[R6 →^{tex} “

R6”]

[Con1 →^{tex} “

Con1”]

[Con2 →^{tex} “

Con2”]

[Dis1 →^{tex} “

Dis1”]

[Dis2 →^{tex} “

Dis2”]

[Con →^{tex} “

Con”]

[T0 →^{tex} “

T0”]

[T1 →^{tex} “

T1”]

[H1 →^{tex} “

H1”]

[H2 →^{tex} “

H2”]

[H0a →^{tex} “

H0a”]

[H0b →^{tex} “

H0b”]

[x < y →^{tex} “#1.

< #2.”]

[x ≤ y →^{tex} “#1.

\leq #2.”]

[x ≮ y →^{tex} “#1.

\nless #2.”]

[x > y →^{tex} “#1.

> #2.”]

[x ≥ y →^{tex} “#1.

\geq #2.”]

[x ≯ y →^{tex} “#1.

\ngtr #2.”]

[x ≠ y →^{tex} “#1.

\neq #2.”]

[x … →^{tex} “#1.

\ldots”]

[x ∧ y →^{tex} “#1.

\wedge #2.”]

[x ∨ y →^{tex} “#1.

\vee #2.”]

[x∧y →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[x∧y ¨= ¬(x ⇒ y)]⌉)] [x∨y →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[x∨ y ¨= (¬x) ⇒ y]⌉)]

3.1 Variables

4 Numerals

[x ≠ y →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[x ≠ y ¨= ¬(x = y)]⌉)]

[\overline{0} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{0} ¨= 0]⌉)] [\overline{1} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{1} ¨= 0′]⌉)]

[\overline{2} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{2} ¨= 0′′]⌉)] [\overline{3} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{3} ¨= 0′′′]⌉)]

[\overline{4} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{4} ¨= 0′′′′]⌉)] [\overline{5} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{5} ¨= 0′′′′′]⌉)]

[\overline{6} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{6} ¨= 0′′′′′′]⌉)] [\overline{7} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{7} ¨=

0′′′′′′′]⌉)] [\overline{8} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{8} ¨= 0′′′′′′′′]⌉)] [\overline{9} →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[\overline{9} ¨=

0′′′′′′′′′]⌉)]

[\overline{0} →^{tex} “

\overline\{0\}”] [\overline{1} →^{tex} “ \overline\{1\}”] [\overline{2} →^{tex} “ \overline\{2\}”] [\overline{3} →^{tex} “ \overline\{3\}”] [\overline{4} →^{tex} “ \overline\{4\}”] [\overline{5} →^{tex} “ \overline\{5\}”] [\overline{6} →^{tex} “ \overline\{6\}”] [\overline{7} →^{tex} “ \overline\{7\}”] [\overline{8} →^{tex} “ \overline\{8\}”] [\overline{9} →^{tex} “ \overline{9}”]

[∃x: y →^{macro} λt.λs.λc.M̃_{4}(t, s, c, ⌈[∃x: y ¨= ¬(∀x: ¬y)]⌉)]

5 Priority table

[frozen →^{prio} Preassociative [frozen], [base], [bracket ∗ end bracket], [big bracket ∗ end bracket], [ $ ∗ $ ], [flush left [∗]], [x], [y], [z], [[∗ ▷◁ ∗]], [[∗ →^{∗} ∗]], [pyk], [tex], [name], [prio], [∗], [T], [if(∗, ∗, ∗)], [[∗ ⇒^{∗} ∗]], [val], [claim], [⊥], [f(∗)], [(∗)^{I}], [F], [\underline{0}], [\underline{1}], [\underline{2}], [\underline{3}], [\underline{4}], [\underline{5}], [\underline{6}], [\underline{7}], [\underline{8}], [\underline{9}], [0], [1], [2], [3], [4], [5], [6], [7], [8], [9], [a], [b], [c], [d], [e], [f], [g], [h], [i], [j], [k], [l], [m], [n], [o], [p], [q], [r], [s], [t], [u], [v], [w], [(∗)^{M}], [If(∗, ∗, ∗)], [array{∗} ∗ end array], [l], [c], [r], [empty], [⟨∗ | ∗:= ∗⟩], [M(∗)], [Ũ(∗)], [U(∗)], [U^{M}(∗)], [apply(∗, ∗)], [apply_{1}(∗, ∗)], [identifier(∗)], [identifier_{1}(∗, ∗)], [arrayplus(∗, ∗)], [array-remove(∗, ∗, ∗)], [array-put(∗, ∗, ∗, ∗)], [array-add(∗, ∗, ∗, ∗, ∗)], [bit(∗, ∗)], [bit_{1}(∗, ∗)], [rack], ["vector"], ["bibliography"], ["dictionary"], ["body"], ["codex"], ["expansion"], ["code"], ["cache"], ["diagnose"], ["pyk"], ["tex"], ["texname"], ["value"], ["message"], ["macro"], ["definition"], ["unpack"], ["claim"], ["priority"], ["lambda"], ["apply"], ["true"], ["if"], ["quote"], ["proclaim"], ["define"], ["introduce"], ["hide"], ["pre"], ["post"], [E(∗, ∗, ∗)], [E_{2}(∗, ∗, ∗, ∗, ∗)], [E_{3}(∗, ∗, ∗, ∗)], [E_{4}(∗, ∗, ∗, ∗)], [lookup(∗, ∗, ∗)], [abstract(∗, ∗, ∗, ∗)], [⌈∗⌉], [M(∗, ∗, ∗)], [M_{2}(∗, ∗, ∗, ∗)], [M^{∗}(∗, ∗, ∗)], [macro], [s_{0}], [zip(∗, ∗)], [assoc_{1}(∗, ∗, ∗)], [(∗)^{p}], [self], [[∗ ¨= ∗]], [[∗ ˙= ∗]], [[∗ ´= ∗]], [[∗ =^{pyk} ∗]], [[∗ =^{tex} ∗]], [[∗ =^{name} ∗]], [Priority table[∗]], [M̃_{1}], [M̃_{2}(∗)], [M̃_{3}(∗)], [M̃_{4}(∗, ∗, ∗, ∗)], [M̃(∗, ∗, ∗)], [Q̃(∗, ∗, ∗)], [Q̃_{2}(∗, ∗, ∗)], [Q̃_{3}(∗, ∗, ∗, ∗)], [Q̃^{∗}(∗, ∗, ∗)], [(∗)], [(∗)], [display(∗)], [statement(∗)], [[∗]^{·}], [[∗]^{−}], [aspect(∗, ∗)], [aspect(∗, ∗, ∗)], [⟨∗⟩], [tuple_{1}(∗)], [tuple_{2}(∗)], [let_{2}(∗, ∗)], [let_{1}(∗, ∗)], [[∗ =^{claim} ∗]], [checker], [check(∗, ∗)], [check_{2}(∗, ∗, ∗)], [check_{3}(∗, ∗, ∗)], [check^{∗}(∗, ∗)], [check_{2}^{∗}(∗, ∗, ∗)], [[∗]^{·}], [[∗]^{−}], [[∗]^{∘}], [msg], [[∗ =^{msg} ∗]], [<stmt>], [stmt], [[∗ =^{stmt} ∗]], [HeadNil′], [HeadPair′], [Transitivity′], [⊥ ⊥], [Contra′], [T′_{E}], [L_{1}], [\underline{∗}], [A], [B], [C], [D], [E], [F], [G], [H], [I], [J], [K], [L], [M], [N], [O], [P], [Q], [R], [S], [T ], [U], [V], [W], [X], [Y], [Z], [⟨∗ | ∗:= ∗⟩], [⟨^{∗}∗ | ∗:= ∗⟩], [∅], [Remainder], [(∗)^{v}], [intro(∗, ∗, ∗, ∗)], [intro(∗, ∗, ∗)], [error(∗, ∗)], [error_{2}(∗, ∗)], [proof(∗, ∗, ∗)], [proof_{2}(∗, ∗)], [S(∗, ∗)], [S^{I}(∗, ∗)], [S^{⊳} (∗, ∗)], [S_{1}^{⊳} (∗, ∗, ∗)], [S^{E}(∗, ∗)], [S_{1}^{E}(∗, ∗, ∗)], [S^{+}(∗, ∗)], [S_{1}^{+}(∗, ∗, ∗)], [S^{−}(∗, ∗)], [S_{1}^{−}(∗, ∗, ∗)], [S^{∗}(∗, ∗)], [S_{1}^{∗}(∗, ∗, ∗)], [S_{2}^{∗}(∗, ∗, ∗, ∗)], [S^{@}(∗, ∗)], [S_{1}^{@}(∗, ∗, ∗)], [S^{⊢}(∗, ∗)], [S_{1}^{⊢}(∗, ∗, ∗, ∗)], [S⊢ ⊢(∗, ∗)],

[S⊢ ⊢ ; 1(∗, ∗, ∗, ∗)], [S^{i.e.}(∗, ∗)], [S_{1}^{i.e.}(∗, ∗, ∗, ∗)], [S_{2}^{i.e.}(∗, ∗, ∗, ∗, ∗)], [S^{∀}(∗, ∗)],

[S_{1}^{∀}(∗, ∗, ∗, ∗)], [S^{;}(∗, ∗)], [S_{1}^{;}(∗, ∗, ∗)], [S_{2}^{;}(∗, ∗, ∗, ∗)], [T (∗)], [claims(∗, ∗, ∗)], [claims_{2}(∗, ∗, ∗)], [<proof>], [proof], [[Lemma ∗: ∗]], [[Proof of ∗: ∗]], [[∗ lemma ∗: ∗]], [[∗ antilemma ∗: ∗]], [[∗ rule ∗: ∗]], [[∗ antirule ∗: ∗]], [verifier], [V_{1}(∗)], [V_{2}(∗, ∗)], [V_{3}(∗, ∗, ∗, ∗)], [V_{4}(∗, ∗)], [V_{5}(∗, ∗, ∗, ∗)], [V_{6}(∗, ∗, ∗, ∗)], [V_{7}(∗, ∗, ∗, ∗)], [Cut(∗, ∗)], [Head_{⊕}(∗)], [Tail_{⊕}(∗)], [rule_{1}(∗, ∗)], [rule(∗, ∗)], [Rule tactic], [Plus(∗, ∗)], [[Theory ∗]], [theory_{2}(∗, ∗)], [theory_{3}(∗, ∗)], [theory_{4}(∗, ∗, ∗)], [HeadNil′′], [HeadPair′′], [Transitivity′′], [Contra′′], [HeadNil], [HeadPair], [Transitivity], [Contra], [T_{E}], [ragged right], [ragged right expansion ], [parm(∗, ∗, ∗)], [parm^{∗}(∗, ∗, ∗)], [inst(∗, ∗)], [inst^{∗}(∗, ∗)], [occur(∗, ∗, ∗)], [occur^{∗}(∗, ∗, ∗)], [unify(∗ = ∗, ∗)], [unify^{∗}(∗ = ∗, ∗)], [unify_{2}(∗ = ∗, ∗)], [L_{a}], [L_{b}], [L_{c}], [L_{d}], [L_{e}], [L_{f}], [L_{g}], [L_{h}], [L_{i}], [L_{j}], [L_{k}], [L_{l}], [L_{m}], [L_{n}], [L_{o}], [L_{p}], [L_{q}], [L_{r}], [L_{s}], [L_{t}], [L_{u}], [L_{v}], [L_{w}], [L_{x}], [L_{y}], [L_{z}], [L_{A}], [L_{B}], [L_{C}], [L_{D}], [L_{E}], [L_{F}], [L_{G}], [L_{H}], [L_{I}], [L_{J}], [L_{K}], [L_{L}], [L_{M}], [L_{N}], [L_{O}], [L_{P}], [L_{Q}], [L_{R}], [L_{S}], [L_{T}], [L_{U}], [L_{V}], [L_{W}], [L_{X}], [L_{Y}], [L_{Z}], [L_{?}], [Reflexivity], [Reflexivity_{1}], [Commutativity], [Commutativity_{1}], [<tactic>], [tactic], [[∗ =^{tactic} ∗]], [P(∗, ∗, ∗)], [P^{∗}(∗, ∗, ∗)], [p_{0}], [conclude_{1}(∗, ∗)], [conclude_{2}(∗, ∗, ∗)], [conclude_{3}(∗, ∗, ∗, ∗)], [conclude_{4}(∗, ∗)], [check], [[∗ =^{∘} ∗]], [RootVisible(∗)], [A], [R], [C], [T], [L], [\{∗\}], [\overline{∗}], [a], [b], [c], [d], [e], [f ], [g], [h], [i], [j ], [k], [l], [m], [n], [o], [p], [q], [r], [s], [t], [u], [v], [w], [x], [y], [z], [⟨∗≡ ∗ | ∗:=∗⟩], [⟨∗≡^{0} ∗ | ∗:=∗⟩], [⟨∗≡^{1} ∗ | ∗:=∗⟩], [⟨∗≡^{∗} ∗ | ∗:=∗⟩], [Ded(∗, ∗)], [Ded_{0}(∗, ∗)], [Ded_{1}(∗, ∗, ∗)], [Ded_{2}(∗, ∗, ∗)], [Ded_{3}(∗, ∗, ∗, ∗)], [Ded_{4}(∗, ∗, ∗, ∗)], [Ded_{4}^{∗}(∗, ∗, ∗, ∗)], [Ded_{5}(∗, ∗, ∗)], [Ded_{6}(∗, ∗, ∗, ∗)], [Ded_{6}^{∗}(∗, ∗, ∗, ∗)], [Ded_{7}(∗)], [Ded_{8}(∗, ∗)], [Ded_{8}^{∗}(∗, ∗)], [S], [Neg], [MP], [Gen], [Ded], [S1], [S2], [S3], [S4], [S5], [S6], [S7], [S8], [S9], [Repetition], [A1′], [A2′], [A4′], [A5′], [Prop 3.2a], [Prop 3.2b], [Prop 3.2c], [Prop 3.2d], [Prop 3.2e_{1}], [Prop 3.2e_{2}], [Prop 3.2e], [Prop 3.2f_{1}], [Prop 3.2f_{2}], [Prop 3.2f], [Prop 3.2g_{1}], [Prop 3.2g_{2}], [Prop 3.2g], [Prop 3.2h_{1}], [Prop 3.2h_{2}], [Prop 3.2h], [Block_{1}(∗, ∗, ∗)], [Block_{2}(∗)], [\overline{0}], [\overline{1}], [\overline{2}], [\overline{3}], [\overline{4}], [\overline{5}], [\overline{6}], [\overline{7}], [\overline{8}], [\overline{9}], [rule div], [R], [R1], [R2], [R3], [R4], [R5], [R6], [Con1], [Con2], [Con], [Dis1], [Dis2], [T1], [T0], [H0a], [H0b], [H1], [H2], [S10], [Prop 3.2], [Prop 3.2i], [Prop 3.2j_{1}], [Prop 3.2j_{2}], [Prop 3.2j], [Prop 3.2k_{1}], [Prop 3.2k_{2}], [Prop 3.2k], [Prop 3.2l_{1}], [Prop 3.2l_{2}], [Prop 3.2l], [Prop 3.2m_{1}], [Prop 3.2m_{2}], [Prop 3.2m], [Prop 3.2n_{1}], [Prop 3.2n_{2}], [Prop 3.2n], [Prop 3.2o], [Prop 3.4], [Prop 3.4a_{1}], [Prop 3.4a_{2}], [Prop 3.4a], [Prop 3.4b], [Prop 3.4c_{1}], [Prop 3.4c_{2}], [Prop 3.4c], [Prop 3.4d_{1}], [Prop 3.4d_{2}], [Prop 3.4d], [Prop 3.5], [Prop 3.5a], [Prop 3.5b], [Prop 3.5c], [Prop 3.5d_{1}], [Prop 3.5d_{2}], [Prop 3.5d], [Prop 3.5e_{1}], [Prop 3.5e_{2}], [Prop 3.5e], [Prop 3.5f_{1}], [Prop 3.5f_{2}], [Prop 3.5f], [Prop 3.5g_{1}], [Prop 3.5g_{2}], [Prop 3.5g], [Prop 3.5h_{1}], [Prop 3.5h_{2}], [Prop 3.5h], [Prop 3.5i_{1}], [Prop 3.5i_{2}], [Prop 3.5i], [Prop 3.5j_{1}], [Prop 3.5j_{2}], [Prop 3.5j], [Prop 3.7], [Prop 3.7a], [Prop 3.7b], [Prop 3.7c], [Prop 3.7d], [Prop 3.7e], [Prop 3.7f], [Prop 3.7g], [Prop 3.7g′], [Prop 3.7h], [Prop 3.7i], [Prop 3.7j], [Prop 3.7k], [Prop 3.7k′], [Prop 3.7l], [Prop 3.7l′], [Prop 3.7m], [Prop 3.7n], [Prop 3.7o], [Prop 3.7p], [Prop 3.7q], [Prop 3.7r], [Prop 3.7s], [Prop 3.7t], [Prop 3.7u], [Prop 3.7u′], [Prop 3.7v], [Prop 3.7w], [Prop 3.7x], [Prop 3.7x′], [Prop 3.7y], [Prop 3.7y′], [Prop 3.7z], [Prop 3.7z′], [Prop 3.10], [Prop 3.10a], [Prop 3.10b], [Prop 3.10c], [Prop 3.10d], [Prop 3.10e], [Prop 3.10f], [Prop 3.10g], [Prop 3.10h], [Prop 3.11]; Preassociative [∗ {∗}], [∗/indexintro(∗, ∗, ∗, ∗)], [∗/intro(∗, ∗, ∗)], [∗/bothintro(∗, ∗, ∗, ∗, ∗)], [∗/nameintro(∗, ∗, ∗, ∗)], [∗′], [∗[ ∗]], [∗[∗→∗]], [∗[∗⇒∗]], [∗0], [∗1], [0b], [∗-color(∗)], [∗-color^{∗}(∗)], [∗^{H}], [∗^{T}], [∗^{U}], [∗^{h}], [∗^{t}], [∗^{s}], [∗^{c}], [∗^{d}], [∗^{a}], [∗^{C}], [∗^{M}], [∗^{B}], [∗^{r}], [∗^{i}], [∗^{d}], [∗^{R}], [∗^{0}], [∗^{1}], [∗^{2}], [∗^{3}], [∗^{4}], [∗^{5}], [∗^{6}], [∗^{7}], [∗^{8}], [∗^{9}], [∗^{E}], [∗^{V}], [∗^{C}], [∗^{C^{∗}}], [∗^{hide}]; Preassociative [“ ∗ ”], [], [(∗)^{t}], [string(∗) + ∗], [string(∗) ++ ∗], [ ∗], [ ∗], [!∗], ["∗], [#∗], [$∗], [%∗], [&∗], [’∗], [(∗], [)∗], [∗∗], [+∗], [, ∗], [-∗], [.∗], [/∗], [0∗], [1∗], [2∗], [3∗], [4∗], [5∗], [6∗], [7∗], [8∗], [9∗], [:∗], [; ∗], [<∗], [=∗], [>∗], [?∗], [@∗], [A∗], [B∗], [C∗], [D∗], [E∗], [F∗], [G∗], [H∗], [I∗], [J∗], [K∗], [L∗], [M∗], [N∗], [O∗], [P∗], [Q∗], [R∗], [S∗], [T∗], [U∗], [V∗], [W∗], [X∗], [Y∗], [Z∗], [[∗], [\∗], []∗], [ˆ ∗], [ ∗], [‘∗], [a∗], [b∗], [c∗], [d∗], [e∗], [f∗], [g∗], [h∗], [i∗], [j∗], [k∗], [l∗], [m∗], [n∗], [o∗], [p∗], [q∗], [r∗], [s∗], [t∗], [u∗], [v∗], [w∗], [x∗], [y∗], [z∗], [{∗], [|∗], [}∗], [˜ ∗], [Preassociative ∗; ∗], [Postassociative ∗; ∗], [[∗], ∗], [priority ∗ end], [newline ∗], [macro newline ∗], [MacroIndent(∗)]; Preassociative [∗ ’ ∗], [∗ ‘ ∗]; Preassociative [∗′]; Preassociative [∗ · ∗], [∗ ·_{0} ∗]; Preassociative [∗ + ∗], [∗ +_{0} ∗], [∗ +_{1} ∗], [∗ − ∗], [∗ −_{0} ∗], [∗ −_{1} ∗]; Preassociative [∗ ∪ {∗}], [∗ ∪ ∗], [∗\{∗}]; Postassociative [∗ ˙. . ∗], [∗ \underline{˙. .} ∗], [∗ \underline{: :} ∗], [∗ \underline{+2∗} ∗], [∗ : : ∗], [∗ +2∗ ∗]; Postassociative [∗, ∗]; Preassociative

[∗ ≈^{B} ∗], [∗ ≈^{D} ∗], [∗ ≈^{C} ∗], [∗ ≈^{P} ∗], [∗ ≈ ∗], [∗ = ∗], [∗ →^{+} ∗], [∗ =^{t} ∗], [∗ =^{t^{∗}} ∗], [∗ =^{r} ∗],

[∗ ∈_{t} ∗], [∗ ⊆_{T} ∗], [∗ =^{T} ∗], [∗ =^{s} ∗], [∗ free in ∗], [∗ free in^{∗} ∗], [∗ free for ∗ in ∗], [∗ free for^{∗} ∗ in ∗], [∗ ∈_{c} ∗], [∗ < ∗], [∗ <′ ∗], [∗ ≤′ ∗], [∗ = ∗], [∗ ≠ ∗], [∗^{var}], [∗#^{0}∗], [∗#^{1}∗], [∗#^{∗}∗], [∗ < ∗], [∗ ≤ ∗], [∗ ≮ ∗], [∗ > ∗], [∗ ≥ ∗], [∗ ≯ ∗], [∗ ≠ ∗]; Preassociative [¬∗]; Preassociative [∗ ∧ ∗], [∗ ¨∧ ∗], [∗ ˜∧ ∗], [∗ ∧_{c} ∗], [∗ ∧ ∗]; Preassociative [∗ ∨ ∗], [∗ ∥ ∗], [∗ ¨∨ ∗], [∗ ∨ ∗]; Preassociative [∃∗: ∗], [∀∗: ∗], [∀_{obj}∗: ∗], [∃∗: ∗]; Postassociative [∗ ¨⇒ ∗], [∗ ⇒ ∗], [∗ ⇔ ∗]; Postassociative [∗ : ∗], [∗ spy ∗], [∗!∗]; Preassociative

[∗ \{ \begin{matrix}∗ \\ ∗ \end{matrix} ];

Preassociative [λ ∗ .∗], [Λ ∗ .∗], [Λ∗], [if ∗ then ∗ else ∗], [let ∗ = ∗ in ∗], [let ∗ ¨= ∗ in ∗]; Preassociative [∗#∗]; Preassociative [∗^{I}], [∗^{⊳} ], [∗^{V}], [∗^{+}], [∗^{−}], [∗^{∗}]; Preassociative [∗ @ ∗], [∗ ⊳ ∗], [∗ ⊳ ⊳ ∗], [∗ ≫ ∗], [∗ ⊵ ∗]; Postassociative [∗ ⊢ ∗], [∗ ⊢⊢ ∗], [∗ i.e. ∗]; Preassociative [∀∗: ∗], [Π∗: ∗]; Postassociative [∗ ⊕ ∗]; Postassociative [∗; ∗]; Preassociative [∗ proves ∗]; Preassociative [∗ proof of ∗ : ∗], [Line ∗ : ∗ ≫ ∗; ∗], [Last line ∗ ≫ ∗ □], [Line ∗ : Premise ≫ ∗; ∗], [Line ∗ : Side-condition ≫ ∗; ∗], [Arbitrary ≫ ∗; ∗], [Local ≫ ∗ = ∗; ∗], [Begin ∗; ∗ : End; ∗], [Last block line ∗ ≫ ∗; ], [Arbitrary ≫ ∗; ∗]; Postassociative [∗ | ∗]; Postassociative [∗ , ∗], [∗[ ∗]∗]; Preassociative [∗&∗], [→]; Preassociative [∗\\∗], [∗ linebreak[4] ∗], [∗\\∗], [∗ | ∗], [∗ …]; ]

18