Nuprl Lemma : map-upto
∀[n:ℕ+]. ∀[f:Top]. (map(f;upto(n)) ~ map(f;upto(n - 1)) @ [f (n - 1)])
Proof
Definitions occuring in Statement :
upto: upto(n),
map: map(f;as),
append: as @ bs,
cons: [a / b],
nil: [],
nat_plus: ℕ+,
uall: ∀[x:A]. B[x],
top: Top,
apply: f a,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
all: ∀x:A. B[x]
Lemmas referenced :
upto_decomp1,
map_append_sq,
map_cons_lemma,
map_nil_lemma,
top_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
sqequalAxiom,
because_Cache
Latex:
\mforall{}[n:\mBbbN{}\msupplus{}]. \mforall{}[f:Top]. (map(f;upto(n)) \msim{} map(f;upto(n - 1)) @ [f (n - 1)])
Date html generated:
2016_05_15-PM-04_35_24
Last ObjectModification:
2015_12_27-PM-02_45_59
Theory : general
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