Nuprl Lemma : map_id
∀[A:Type]. ∀[as:A List]. (map(Id{A};as) = as ∈ (A List))
Proof
Definitions occuring in Statement :
map: map(f;as),
list: T List,
tidentity: Id{T},
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
top: Top,
tidentity: Id{T},
identity: Id,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
equal_wf,
list_wf,
map_wf,
tidentity_wf,
map_nil_lemma,
nil_wf,
map_cons_lemma,
squash_wf,
true_wf,
cons_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
rename,
applyEquality,
imageElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
equalityUniverse,
levelHypothesis,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[as:A List]. (map(Id\{A\};as) = as)
Date html generated:
2017_04_14-AM-09_25_40
Last ObjectModification:
2017_02_27-PM-03_59_44
Theory : list_1
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