Nuprl Lemma : no-uniform-xmiddle
¬(∀[P:ℙ]. (P ∨ (¬P)))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
or: P ∨ Q
Definitions unfolded in proof :
not: ¬A,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
so_lambda: λ2x.t[x],
or: P ∨ Q,
so_apply: x[s],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
false: False,
bfalse: ff,
true: True
Lemmas referenced :
uall_wf,
or_wf,
not_wf,
false_wf,
equal_wf,
true_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
universeEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesisEquality,
hypothesis,
rename,
applyEquality,
equalityTransitivity,
equalitySymmetry,
isectEquality,
unionElimination,
voidElimination,
dependent_functionElimination,
independent_functionElimination,
natural_numberEquality
Latex:
\mneg{}(\mforall{}[P:\mBbbP{}]. (P \mvee{} (\mneg{}P)))
Date html generated:
2016_05_15-PM-03_19_09
Last ObjectModification:
2015_12_27-PM-01_03_35
Theory : general
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