Nuprl Lemma : list-diff2-sym
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[as:T List]. ∀[b,c:T]. (as-[b; c] = as-[c]-[b] ∈ (T List))
Proof
Definitions occuring in Statement :
list-diff: as-bs,
cons: [a / b],
nil: [],
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
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,
implies: P ⇒ Q,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
or: P ∨ Q
Lemmas referenced :
equal_wf,
squash_wf,
true_wf,
list-diff_wf,
cons_wf,
nil_wf,
list-diff-diff,
iff_weakening_equal,
list_ind_cons_lemma,
list_ind_nil_lemma,
list-diff_functionality,
cons_member,
member_singleton,
or_wf,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
cumulativity,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
lambdaFormation,
independent_pairFormation,
addLevel,
orFunctionality,
promote_hyp,
unionElimination,
inrFormation,
inlFormation
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[as:T List]. \mforall{}[b,c:T]. (as-[b; c] = as-[c]-[b])
Date html generated:
2017_04_17-AM-09_13_12
Last ObjectModification:
2017_02_27-PM-05_19_54
Theory : decidable!equality
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