Nuprl Lemma : map-conversion-test2
∀[L:ℤ List]. (map(λx.(x + 0);L) ~ map(λx.x;L))
Proof
Definitions occuring in Statement :
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
lambda: λx.A[x],
add: n + m,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
uimplies: b supposing a,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
list_wf,
add-zero,
map_functionality_wrt_sq,
int_subtype_base,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
axiomSqEquality,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
lambdaFormation,
hypothesisEquality,
sqequalRule,
independent_isectElimination,
baseClosed,
dependent_functionElimination,
because_Cache
Latex:
\mforall{}[L:\mBbbZ{} List]. (map(\mlambda{}x.(x + 0);L) \msim{} map(\mlambda{}x.x;L))
Date html generated:
2019_06_20-PM-01_33_27
Last ObjectModification:
2018_08_24-PM-11_47_12
Theory : list_1
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