Nuprl Lemma : cons-wf-fset
∀[T:Type]. ∀[s:fset(T)]. ∀[x:T]. ([x / s] ∈ fset(T))
Proof
Definitions occuring in Statement :
fset: fset(T),
cons: [a / b],
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset: fset(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
or: P ∨ Q
Lemmas referenced :
quotient-member-eq,
list_wf,
set-equal_wf,
set-equal-equiv,
cons_wf,
equal-wf-base,
fset_wf,
or_wf,
equal_wf,
l_member_wf,
cons_member,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productEquality,
cumulativity,
universeEquality,
lambdaFormation,
independent_pairFormation,
addLevel,
equalityTransitivity,
equalitySymmetry,
orFunctionality,
impliesFunctionality
Latex:
\mforall{}[T:Type]. \mforall{}[s:fset(T)]. \mforall{}[x:T]. ([x / s] \mmember{} fset(T))
Date html generated:
2016_05_14-PM-03_39_51
Last ObjectModification:
2015_12_26-PM-06_41_33
Theory : finite!sets
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