Nuprl Lemma : iseg_antisymmetry
∀[T:Type]. ∀[as,bs:T List]. (as = bs ∈ (T List)) supposing (bs ≤ as and as ≤ bs)
Proof
Definitions occuring in Statement :
iseg: l1 ≤ l2,
list: T List,
uimplies: b supposing a,
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],
uimplies: b supposing a,
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
top: Top,
not: ¬A,
false: False,
assert: ↑b,
ifthenelse: if b then t else f fi ,
bfalse: ff,
squash: ↓T,
true: True,
guard: {T}
Lemmas referenced :
list_induction,
uall_wf,
list_wf,
isect_wf,
iseg_wf,
equal_wf,
nil_wf,
equal-wf-base-T,
iseg_nil,
cons_wf,
assert_wf,
null_wf3,
assert_elim,
subtype_rel_list,
top_wf,
null_cons_lemma,
bfalse_wf,
btrue_neq_bfalse,
cons_iseg
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,
because_Cache,
baseClosed,
isect_memberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
rename,
dependent_functionElimination,
productElimination,
addLevel,
independent_isectElimination,
applyEquality,
voidElimination,
voidEquality,
universeEquality,
levelHypothesis,
promote_hyp,
isectEquality,
imageElimination,
natural_numberEquality,
imageMemberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[as,bs:T List]. (as = bs) supposing (bs \mleq{} as and as \mleq{} bs)
Date html generated:
2018_05_21-PM-06_46_23
Last ObjectModification:
2017_07_26-PM-04_56_09
Theory : general
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