Nuprl Lemma : proof-by-cont-implies-LEM
(∀p:ℙ. ((¬¬p) ⇒ p)) ⇒ (∀p:ℙ. (p ∨ (¬p)))
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
not: ¬A,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
or_wf,
not_wf,
not_over_or,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
independent_functionElimination,
productElimination,
independent_isectElimination,
voidElimination,
universeEquality,
instantiate,
sqequalRule,
lambdaEquality,
cumulativity,
functionEquality
Latex:
(\mforall{}p:\mBbbP{}. ((\mneg{}\mneg{}p) {}\mRightarrow{} p)) {}\mRightarrow{} (\mforall{}p:\mBbbP{}. (p \mvee{} (\mneg{}p)))
Date html generated:
2016_05_13-PM-03_46_05
Last ObjectModification:
2015_12_26-AM-09_58_41
Theory : call!by!value_2
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