Nuprl Lemma : reject_cons_hd
∀[T:Type]. ∀[a:T]. ∀[as:T List]. ∀[i:ℤ]. [a / as]\[i] = as ∈ (T List) supposing i ≤ 0
Proof
Definitions occuring in Statement :
reject: as\[i],
cons: [a / b],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
top: Top,
le: A ≤ B,
and: P ∧ Q,
false: False,
guard: {T},
uimplies: b supposing a,
implies: P ⇒ Q,
reject: as\[i],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ
Lemmas referenced :
le_int_wf,
bool_wf,
equal-wf-base,
int_subtype_base,
assert_wf,
le_wf,
reduce_tl_cons_lemma,
lt_int_wf,
less_than_wf,
bnot_wf,
less_than_transitivity1,
less_than_irreflexivity,
uiff_transitivity,
eqtt_to_assert,
assert_of_le_int,
eqff_to_assert,
assert_functionality_wrt_uiff,
bnot_of_le_int,
assert_of_lt_int,
equal_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
hypothesis,
sqequalRule,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
because_Cache,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
Error :universeIsType,
intEquality,
universeEquality,
Error :isect_memberFormation_alt,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a:T]. \mforall{}[as:T List]. \mforall{}[i:\mBbbZ{}]. [a / as]\mbackslash{}[i] = as supposing i \mleq{} 0
Date html generated:
2019_06_20-PM-00_39_08
Last ObjectModification:
2018_09_26-PM-02_07_31
Theory : list_0
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