Nuprl Lemma : not-not-all-int_seg-shift
∀a,b:ℤ. ∀P:{a..b-} ⟶ ℙ. ((∀i:{a..b-}. (¬¬P[i])) ⇒ (¬¬(∀i:{a..b-}. P[i])))
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
function: x:A ⟶ B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
implies: P ⇒ Q,
not: ¬A,
or: P ∨ Q,
false: False,
uall: ∀[x:A]. B[x],
so_apply: x[s],
subtype_rel: A ⊆r B,
prop: ℙ
Lemmas referenced :
not-not-all-int_seg-xmiddle,
int_seg_wf,
istype-void,
subtype_rel_self,
istype-int
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_functionElimination,
unionElimination,
voidElimination,
universeIsType,
isectElimination,
sqequalRule,
functionIsType,
unionIsType,
applyEquality,
because_Cache,
instantiate,
universeEquality,
inhabitedIsType
Latex:
\mforall{}a,b:\mBbbZ{}. \mforall{}P:\{a..b\msupminus{}\} {}\mrightarrow{} \mBbbP{}. ((\mforall{}i:\{a..b\msupminus{}\}. (\mneg{}\mneg{}P[i])) {}\mRightarrow{} (\mneg{}\mneg{}(\mforall{}i:\{a..b\msupminus{}\}. P[i])))
Date html generated:
2020_05_19-PM-09_36_12
Last ObjectModification:
2019_11_04-PM-02_02_56
Theory : int_1
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