Nuprl Lemma : no-excluded-middle-squash
¬↓∀P:ℙ. (P ∨ (¬P))
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
squash: ↓T,
or: P ∨ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
squash: ↓T,
false: False,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q
Lemmas referenced :
no-excluded-middle,
squash_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
imageElimination,
independent_functionElimination,
thin,
hypothesis,
voidElimination,
universeIsType,
instantiate,
isectElimination,
sqequalRule,
functionEquality,
universeEquality,
unionEquality,
cumulativity,
hypothesisEquality
Latex:
\mneg{}\mdownarrow{}\mforall{}P:\mBbbP{}. (P \mvee{} (\mneg{}P))
Date html generated:
2020_05_20-AM-09_07_33
Last ObjectModification:
2020_01_23-PM-05_22_31
Theory : bar!type
Home
Index