Commit c521126b authored by Michael Kohlhase's avatar Michael Kohlhase

weakening includes: connectives do not need ?Logic; only ?Propositions

parent 5fe6a048
......@@ -9,37 +9,41 @@ import rules scala://lf.mmt.kwarc.info❚
fixmeta ur:?LF❚
theory Truth =
include ?Logic
include ?Propositions
true : prop❙
theory TruthND =
include ?Truth❙
include ?Proofs❙
trueI : ⊦ true❙
theory Falsity =
include ?Logic
include ?Propositions
false : prop❙
theory FalsityND =
include ?Falsity❙
include ?Proofs❙
falseE : ⊦ false ⟶ ↯❘# 1 falseE❙
theory Negation =
include ?Logic
include ?Propositions
not : prop ⟶ prop❘# ¬ 1 prec 20❙
theory NegationNDI =
include ?Negation❙
include ?Proofs❙
notI : {F} (⊦ F ⟶ ↯) ⟶ ⊦ ¬ F❘# notI 2❙
theory NegationNDE =
include ?Negation❙
include ?Proofs❙
notE : {F} ⊦ ¬ F ⟶ ⊦ F ⟶ ↯❘# 2 notE 3❘role ForwardRule❙
......@@ -49,17 +53,19 @@ theory NegationND =
theory Conjunction =
include ?Logic
include ?Propositions
and : prop ⟶ prop ⟶ prop❘# 1 ∧ 2 prec 15❙
theory ConjunctionNDI =
include ?Conjunction❙
include ?Proofs❙
andI : {F,G} ⊦ F ⟶ ⊦ G ⟶ ⊦ F ∧ G❙
theory ConjunctionNDE =
include ?Conjunction❙
include ?Proofs❙
andEl : {F,G} ⊦ F ∧ G ⟶ ⊦ F❘# 3 andEl❘role ForwardRule❙
andEr : {F,G} ⊦ F ∧ G ⟶ ⊦ G❘# 3 andEr❘role ForwardRule❙
......@@ -70,18 +76,20 @@ theory ConjunctionND =
theory Disjunction =
include ?Logic
include ?Propositions
or : prop ⟶ prop ⟶ prop❘# 1 ∨ 2 prec 15❙
theory DisjunctionNDI =
include ?Disjunction❙
include ?Proofs❙
orIl : {F,G} ⊦ F ⟶ ⊦ F ∨ G❘# 3 orIl❙
orIr : {F,G} ⊦ G ⟶ ⊦ F ∨ G❘# 3 orIr❙
theory DisjunctionNDE =
include ?Disjunction❙
include ?Proofs❙
orE : {F,G,C} ⊦ F ∨ G ⟶ (⊦ F ⟶ ⊦ C) ⟶ (⊦ G ⟶ ⊦ C) ⟶ ⊦ C❘# 4 orE 5 6❙
......@@ -91,17 +99,19 @@ theory DisjunctionND =
theory Implication =
include ?Logic
include ?Propositions
impl : prop ⟶ prop ⟶ prop❘# 1 %R⇒ 2 prec 10❙
theory ImplicationNDI =
include ?Implication❙
include ?Proofs❙
impI : {F,G} (⊦ F ⟶ ⊦ G) ⟶ ⊦ F ⇒ G❙
theory ImplicationNDE =
include ?Implication❙
include ?Proofs❙
impE : {F,G} ⊦ F ⇒ G ⟶ ⊦ F ⟶ ⊦ G❘# 3 impE 4❘role ForwardRule❙
......@@ -118,17 +128,19 @@ theory ImplicationND =
theory Equivalence =
include ?Logic
include ?Propositions
equiv : prop ⟶ prop ⟶ prop❘# 1 ⇔ 2 prec 10❙
theory EquivalenceNDI =
include ?Equivalence❙
include ?Proofs❙
equivI : {F,G} (⊦ F ⟶ ⊦ G) ⟶ (⊦ G ⟶ ⊦ F) ⟶ ⊦ F ⇔ G❙
theory EquivalenceNDE =
include ?Equivalence❙
include ?Proofs❙
equivEl : {F,G} ⊦ F ⇔ G ⟶ ⊦ F ⟶ ⊦ G❘# 3 equivEl 4❘role ForwardRule❙
equivEr : {F,G} ⊦ F ⇔ G ⟶ ⊦ G ⟶ ⊦ F❘# 3 equivEr 4❘role ForwardRule❙
......@@ -148,7 +160,7 @@ theory EquivalenceND =
theory IPL =
include ?Logic
include ?Propositions
include ?Truth❙
include ?Falsity❙
include ?Negation❙
......
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