Nuprl Lemma : mset_mem_fmap
∀s,s':DSet. ∀f:|s| ⟶ |s'|. ∀x:|s|. ∀a:MSet{s}. ((↑(x ∈b a)) ⇒ (↑((f x) ∈b fs-map(f, a))))
Proof
Definitions occuring in Statement :
fset_map: fs-map(f, a),
mset_mem: mset_mem,
mset: MSet{s},
assert: ↑b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
dset: DSet,
set_car: |p|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
fset_map: fs-map(f, a),
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
dset: DSet,
uimplies: b supposing a,
guard: {T},
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
assert_wf,
mset_mem_wf,
mset_wf,
set_car_wf,
dset_wf,
assert_functionality_wrt_uiff,
fset_of_mset_wf,
mset_map_wf,
fset_of_mset_mem,
mset_mem_map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
setElimination,
rename,
functionEquality,
applyEquality,
independent_isectElimination,
productElimination,
because_Cache,
independent_functionElimination
Latex:
\mforall{}s,s':DSet. \mforall{}f:|s| {}\mrightarrow{} |s'|. \mforall{}x:|s|. \mforall{}a:MSet\{s\}. ((\muparrow{}(x \mmember{}\msubb{} a)) {}\mRightarrow{} (\muparrow{}((f x) \mmember{}\msubb{} fs-map(f, a))))
Date html generated:
2016_05_16-AM-07_50_31
Last ObjectModification:
2015_12_28-PM-06_00_43
Theory : mset
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