Nuprl Lemma : name-morph-flip-face-map
∀I:Cname List. ∀y:nameset(I). ∀a:ℕ2. ∀c1:name-morph(I;[]). ∀v:nameset(I).
((¬(v = y ∈ Cname)) ⇒ (flip(((y:=a) o c1);v) = ((y:=a) o flip(c1;v)) ∈ name-morph(I;[])))
Proof
Definitions occuring in Statement :
name-morph-flip: flip(f;y),
name-comp: (f o g),
face-map: (x:=i),
name-morph: name-morph(I;J),
nameset: nameset(L),
coordinate_name: Cname,
nil: [],
list: T List,
int_seg: {i..j-},
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
natural_number: $n,
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
nameset: nameset(L),
uimplies: b supposing a
Lemmas referenced :
name-morph-flip-face-map1,
name-morph_subtype,
nil_wf,
coordinate_name_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nameset_wf,
nameset_subtype,
list-diff-subset,
name-morph_wf,
int_seg_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
isectElimination,
setElimination,
rename,
because_Cache,
independent_isectElimination,
lambdaEquality,
sqequalRule,
natural_numberEquality
Latex:
\mforall{}I:Cname List. \mforall{}y:nameset(I). \mforall{}a:\mBbbN{}2. \mforall{}c1:name-morph(I;[]). \mforall{}v:nameset(I).
((\mneg{}(v = y)) {}\mRightarrow{} (flip(((y:=a) o c1);v) = ((y:=a) o flip(c1;v))))
Date html generated:
2016_06_16-PM-05_35_18
Last ObjectModification:
2015_12_28-PM-04_38_16
Theory : cubical!sets
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