Nuprl Lemma : l_before_antisymmetry
∀[T:Type]. ∀[l:T List]. ∀[x,y:T]. (¬y before x ∈ l) supposing (x before y ∈ l and no_repeats(T;l))
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
universe: Type
Definitions unfolded in proof :
l_before: x before y ∈ l,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
uiff: uiff(P;Q)
Lemmas referenced :
sublist_wf,
cons_wf,
nil_wf,
no_repeats_wf,
list_wf,
sublist_transitivity,
sublist_nil,
equal_wf,
or_wf,
member_wf,
cons_sublist_cons,
append_overlapping_sublists,
list_ind_cons_lemma,
list_ind_nil_lemma,
no_repeats_iff
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
introduction,
cut,
lambdaFormation,
thin,
because_Cache,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
Error :universeIsType,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
universeEquality,
inlFormation,
independent_pairFormation,
inrFormation,
productElimination,
productEquality,
cumulativity,
unionElimination,
promote_hyp,
independent_isectElimination,
voidEquality
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[x,y:T]. (\mneg{}y before x \mmember{} l) supposing (x before y \mmember{} l and no\_repeats(T;l))
Date html generated:
2019_06_20-PM-01_24_17
Last ObjectModification:
2018_09_26-PM-05_27_58
Theory : list_1
Home
Index