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 :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iseg: l1 ≤ l2,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
top: Top
Lemmas referenced :
length_wf_nat,
equal_wf,
nat_wf,
map_append_sq,
map_wf,
append_wf,
list_wf,
iseg_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
dependent_set_memberEquality,
hypothesis,
introduction,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_pairFormation,
functionExtensionality,
applyEquality,
because_Cache,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
setElimination,
rename,
functionEquality,
universeEquality
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:
2016_10_21-AM-10_33_19
Last ObjectModification:
2016_07_12-AM-05_45_23
Theory : list_1
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