Nuprl Lemma : permutation-s-group_wf
∀[rv:SeparationSpace]. ∀[sepw:∀x:Point(rv). ∀y:{y:Point(rv)| x # y} . x # y]. (Perm(rv) ∈ s-Group)
Proof
Definitions occuring in Statement :
permutation-s-group: Perm(rv),
s-group: s-Group,
ss-sep: x # y,
ss-point: Point(ss),
separation-space: SeparationSpace,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
set: {x:A| B[x]}
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
compose: f o g,
guard: {T},
false: False,
not: ¬A,
ss-eq: x ≡ y,
permutation-s-group: Perm(rv),
uiff: uiff(P;Q),
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
permutation-s-group-sep-or,
ss-sep-symmetry,
ss-sep-irrefl,
ss-sep-or,
or: P ∨ Q,
subtype_rel: A ⊆r B,
fun-sep: fun-sep(ss;A;f;g),
exists: ∃x:A. B[x]
Lemmas referenced :
permutation-ss-point,
istype-void,
ss-point_wf,
ss-eq_weakening,
ss-sep_wf,
ss-eq_wf,
separation-space_wf,
compose_wf,
ss-eq_transitivity,
mk-s-group_wf,
permutation-ss_wf,
permutation-ss-eq-iff,
all_wf,
fun-sep_wf,
permutation-ss-sep,
permutation-s-group-sep-or,
subtype_rel_self,
subtype_rel_function,
exists_wf,
or_wf,
ss-sep-symmetry,
ss-sep-irrefl,
ss-sep-or
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
cut,
sqequalRule,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality_alt,
voidElimination,
hypothesis,
dependent_set_memberEquality_alt,
independent_pairEquality,
lambdaEquality_alt,
hypothesisEquality,
universeIsType,
because_Cache,
lambdaFormation_alt,
dependent_functionElimination,
independent_functionElimination,
independent_pairFormation,
productElimination,
productIsType,
functionIsType,
applyEquality,
setElimination,
rename,
inhabitedIsType,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
setIsType,
dependent_set_memberEquality,
lambdaFormation,
isect_memberEquality,
voidEquality,
functionExtensionality,
independent_isectElimination,
lambdaEquality,
productEquality,
unionEquality,
equalityIsType1,
functionEquality,
instantiate,
setEquality,
unionElimination,
inrEquality,
dependent_pairEquality,
inlEquality
Latex:
\mforall{}[rv:SeparationSpace]. \mforall{}[sepw:\mforall{}x:Point(rv). \mforall{}y:\{y:Point(rv)| x \# y\} . x \# y]. (Perm(rv) \mmember{} s-Group)
Date html generated:
2019_10_31-AM-07_27_55
Last ObjectModification:
2019_09_19-PM-04_31_01
Theory : constructive!algebra
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