Nuprl Lemma : map-map-trivial
∀[L:Top List]. ∀[X:Top ⟶ Top]. (map(λp.(fst(p));map(λx.<x, X[x]>;L)) ~ L)
Proof
Definitions occuring in Statement :
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
so_apply: x[s],
pi1: fst(t),
lambda: λx.A[x],
function: x:A ⟶ B[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
compose: f o g,
pi1: fst(t)
Lemmas referenced :
top_wf,
list_wf,
map-map,
map-id
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
functionEquality,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
voidElimination,
voidEquality
Latex:
\mforall{}[L:Top List]. \mforall{}[X:Top {}\mrightarrow{} Top]. (map(\mlambda{}p.(fst(p));map(\mlambda{}x.<x, X[x]>L)) \msim{} L)
Date html generated:
2016_05_14-AM-07_35_25
Last ObjectModification:
2015_12_26-PM-02_11_21
Theory : list_1
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