Nuprl Lemma : eager-product-map-nil
∀[f:Top]. ∀[as:Top List]. (eager-product-map(f;as;[]) ~ [])
Proof
Definitions occuring in Statement :
eager-product-map: eager-product-map(f;as;bs),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
or: P ∨ Q,
eager-product-map: eager-product-map(f;as;bs),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
cons: [a / b],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
guard: {T},
uimplies: b supposing a,
prop: ℙ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
not: ¬A,
colength: colength(L),
nil: [],
it: ⋅,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
less_than: a < b,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
sq_stable: SqStable(P),
subtract: n - m,
subtype_rel: A ⊆r B
Lemmas referenced :
top_wf,
list-cases,
list_ind_nil_lemma,
istype-void,
product_subtype_list,
list_ind_cons_lemma,
eager_map_append_nil_lemma,
list_wf,
istype-top,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
istype-less_than,
colength-cons-not-zero,
colength_wf_list,
istype-false,
istype-le,
subtract-1-ge-0,
subtype_base_sq,
nat_wf,
set_subtype_base,
le_wf,
int_subtype_base,
spread_cons_lemma,
sq_stable__le,
add-associates,
istype-int,
add-commutes,
add-swap,
zero-add,
le_weakening2,
istype-nat
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
Error :isect_memberEquality_alt,
voidElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
axiomSqEquality,
Error :universeIsType,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :lambdaFormation_alt,
setElimination,
rename,
intWeakElimination,
natural_numberEquality,
independent_isectElimination,
independent_functionElimination,
Error :lambdaEquality_alt,
Error :functionIsTypeImplies,
Error :equalityIstype,
because_Cache,
Error :dependent_set_memberEquality_alt,
independent_pairFormation,
instantiate,
cumulativity,
intEquality,
closedConclusion,
equalityTransitivity,
equalitySymmetry,
imageElimination,
imageMemberEquality,
baseClosed,
applyLambdaEquality,
applyEquality,
minusEquality,
baseApply,
sqequalBase
Latex:
\mforall{}[f:Top]. \mforall{}[as:Top List]. (eager-product-map(f;as;[]) \msim{} [])
Date html generated:
2019_06_20-PM-00_44_38
Last ObjectModification:
2018_11_25-PM-09_52_21
Theory : omega
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