Nuprl Lemma : finite-double-negation-shift-extract
∀[A:ℙ]. ∀[B:ℕ ⟶ ℙ]. ∀n:ℕ. ((∀i:ℕn. (((B i) ⇒ A) ⇒ A)) ⇒ ((∀i:ℕn. (B i)) ⇒ A) ⇒ A)
Proof
Definitions occuring in Statement :
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n
Definitions unfolded in proof :
member: t ∈ T,
finite-double-negation-shift,
natrec: natrec,
genrec: genrec,
so_apply: x[s1;s2],
decidable__equal_int,
decidable__int_equal,
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
so_apply: x[s1;s2;s3;s4],
so_lambda: λ2x.t[x],
top: Top,
so_apply: x[s],
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
any: any x,
subtract: n - m,
so_lambda: λ2x y.t[x; y],
iff_weakening_equal,
genrec-ap: genrec-ap
Lemmas referenced :
finite-double-negation-shift,
lifting-strict-int_eq,
top_wf,
equal_wf,
has-value_wf_base,
base_wf,
is-exception_wf,
lifting-strict-spread,
decidable__equal_int,
decidable__int_equal,
iff_weakening_equal
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
isectElimination,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueDecide,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
unionEquality,
unionElimination,
sqleReflexivity,
dependent_functionElimination,
independent_functionElimination,
baseApply,
closedConclusion,
decideExceptionCases,
inrFormation,
because_Cache,
imageMemberEquality,
imageElimination,
exceptionSqequal,
inlFormation,
callbyvalueApply,
applyExceptionCases
Latex:
\mforall{}[A:\mBbbP{}]. \mforall{}[B:\mBbbN{} {}\mrightarrow{} \mBbbP{}]. \mforall{}n:\mBbbN{}. ((\mforall{}i:\mBbbN{}n. (((B i) {}\mRightarrow{} A) {}\mRightarrow{} A)) {}\mRightarrow{} ((\mforall{}i:\mBbbN{}n. (B i)) {}\mRightarrow{} A) {}\mRightarrow{} A)
Date html generated:
2017_10_01-AM-09_10_26
Last ObjectModification:
2017_07_26-PM-04_46_57
Theory : general
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