Nuprl Lemma : fpf-single_wf
∀[A:𝕌{j}]. ∀[B:A ⟶ Type]. ∀[x:A]. ∀[v:B[x]]. (x : v ∈ x:A fp-> B[x])
Proof
Definitions occuring in Statement :
fpf-single: x : v,
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fpf-single: x : v,
fpf: a:A fp-> B[a],
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
cons_wf,
nil_wf,
l_member_wf,
member_singleton,
subtype_rel_self,
subtype_rel_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
dependent_functionElimination,
productElimination,
independent_functionElimination,
applyEquality,
equalitySymmetry,
functionExtensionality,
hyp_replacement,
applyLambdaEquality,
setEquality,
functionEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
isect_memberEquality
Latex:
\mforall{}[A:\mBbbU{}\{j\}]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:A]. \mforall{}[v:B[x]]. (x : v \mmember{} x:A fp-> B[x])
Date html generated:
2018_05_21-PM-09_24_24
Last ObjectModification:
2018_02_09-AM-10_19_50
Theory : finite!partial!functions
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