Nuprl Lemma : uall_instance_test
∀[F:Type ⟶ ℤ ⟶ ℤ ⟶ ℙ]. ∀x:∀[A:Type]. ∀[m,c:ℤ]. F[A;m;c]. ∀B:Type. ∀n,b:ℤ. (x ∈ F[B;n;b])
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3],
all: ∀x:A. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
isect_wf,
equal_wf,
uall_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesisEquality,
applyEquality,
sqequalRule,
lambdaEquality,
isectElimination,
equalityTransitivity,
equalitySymmetry,
hypothesis,
thin,
lemma_by_obid,
sqequalHypSubstitution,
intEquality,
dependent_functionElimination,
independent_functionElimination,
isectEquality,
universeEquality,
cumulativity,
instantiate,
axiomEquality,
because_Cache,
functionEquality
Latex:
\mforall{}[F:Type {}\mrightarrow{} \mBbbZ{} {}\mrightarrow{} \mBbbZ{} {}\mrightarrow{} \mBbbP{}]. \mforall{}x:\mforall{}[A:Type]. \mforall{}[m,c:\mBbbZ{}]. F[A;m;c]. \mforall{}B:Type. \mforall{}n,b:\mBbbZ{}. (x \mmember{} F[B;n;b])
Date html generated:
2016_05_13-PM-03_19_37
Last ObjectModification:
2015_12_26-AM-09_07_42
Theory : subtype_0
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