Nuprl Lemma : iseg_map
∀[A,B:Type]. ∀f:A ⟶ B. ∀L1,L2:A List. (L1 ≤ L2 ⇒ map(f;L1) ≤ map(f;L2))
Proof
Definitions occuring in Statement :
iseg: 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 :
iseg: l1 ≤ l2,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
top: Top
Lemmas referenced :
exists_wf,
list_wf,
equal_wf,
map_wf,
append_wf,
map_append_sq
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
hypothesis,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality,
functionEquality,
inhabitedIsType,
universeIsType,
universeEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_pairFormation
Latex:
\mforall{}[A,B:Type]. \mforall{}f:A {}\mrightarrow{} B. \mforall{}L1,L2:A List. (L1 \mleq{} L2 {}\mRightarrow{} map(f;L1) \mleq{} map(f;L2))
Date html generated:
2019_10_15-AM-10_58_23
Last ObjectModification:
2018_09_27-AM-09_47_05
Theory : list!
Home
Index