Nuprl Lemma : subset-map
∀[A,B:Type]. ∀f:A ⟶ B. ∀L1,L2:A List. (l_subset(A;L1;L2) ⇒ l_subset(B;map(f;L1);map(f;L2)))
Proof
Definitions occuring in Statement :
l_subset: l_subset(T;as;bs),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
l_subset: l_subset(T;as;bs),
implies: P ⇒ Q,
exists: ∃x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
cand: A c∧ B,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
guard: {T}
Lemmas referenced :
l_member_wf,
equal_wf,
exists_wf,
all_wf,
member_map,
map_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
independent_pairFormation,
hypothesis,
productEquality,
introduction,
extract_by_obid,
isectElimination,
applyEquality,
sqequalRule,
lambdaEquality,
functionEquality,
addLevel,
independent_functionElimination,
dependent_functionElimination,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}f:A {}\mrightarrow{} B. \mforall{}L1,L2:A List. (l\_subset(A;L1;L2) {}\mRightarrow{} l\_subset(B;map(f;L1);map(f;L2)))
Date html generated:
2019_06_20-PM-01_33_11
Last ObjectModification:
2018_08_24-PM-10_52_24
Theory : list_1
Home
Index