Nuprl Lemma : sub-mset-map
∀[A,B:Type]. ∀f:A ⟶ B. ∀L1,L2:A List. (sub-mset(A; L1; L2) ⇒ sub-mset(B; map(f;L1); map(f;L2)))
Proof
Definitions occuring in Statement :
sub-mset: sub-mset(T; L1; L2),
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],
implies: P ⇒ Q,
sub-mset: sub-mset(T; L1; L2),
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
top: Top
Lemmas referenced :
map_wf,
permutation_wf,
append_wf,
sub-mset_wf,
list_wf,
map_append_sq,
permutation-map
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
cut,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
functionEquality,
universeEquality,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}f:A {}\mrightarrow{} B. \mforall{}L1,L2:A List. (sub-mset(A; L1; L2) {}\mRightarrow{} sub-mset(B; map(f;L1); map(f;L2)))
Date html generated:
2016_05_15-PM-04_32_18
Last ObjectModification:
2015_12_27-PM-02_49_09
Theory : general
Home
Index