Nuprl Lemma : not-excluded-middle-thru-continuity
¬(∀P:ℙ. (P ∨ (¬P)))
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
not: ¬A,
or: P ∨ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
or: P ∨ Q,
so_apply: x[s]
Lemmas referenced :
not_wf,
or_wf,
all_wf,
nat_wf,
equal-wf-T-base,
not-decidable-zero-sequence
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
dependent_functionElimination,
isectElimination,
functionEquality,
hypothesisEquality,
baseClosed,
voidElimination,
instantiate,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity
Latex:
\mneg{}(\mforall{}P:\mBbbP{}. (P \mvee{} (\mneg{}P)))
Date html generated:
2016_05_14-PM-09_46_08
Last ObjectModification:
2016_01_15-PM-10_56_01
Theory : continuity
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