Nuprl Lemma : face-compatible-symmetry
∀[X:CubicalSet]. ∀[I:Cname List]. ∀[f1,f2:I-face(X;I)]. (face-compatible(X;I;f1;f2) ⇒ face-compatible(X;I;f2;f1))
Proof
Definitions occuring in Statement :
face-compatible: face-compatible(X;I;f1;f2),
I-face: I-face(X;I),
cubical-set: CubicalSet,
coordinate_name: Cname,
list: T List,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
I-face: I-face(X;I),
face-compatible: face-compatible(X;I;f1;f2),
spreadn: spread3,
not: ¬A,
coordinate_name: Cname,
int_upper: {i...},
squash: ↓T,
guard: {T},
false: False,
int_seg: {i..j-},
nameset: nameset(L),
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
sq_type: SQType(T)
Lemmas referenced :
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformeq_wf,
itermVar_wf,
intformnot_wf,
int_formula_prop_and_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_not_lemma,
le_wf,
int_formula_prop_wf,
equal_wf,
coordinate_name_wf,
not_wf,
face-compatible_wf,
I-face_wf,
list_wf,
cubical-set_wf,
subtype_base_sq,
list_subtype_base,
set_subtype_base,
int_subtype_base,
squash_wf,
true_wf,
list-diff_wf,
cname_deq_wf,
cons_wf,
nil_wf,
list-diff2-sym,
iff_weakening_equal,
list-diff2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
introduction,
sqequalHypSubstitution,
productElimination,
thin,
sqequalRule,
lambdaEquality,
axiomEquality,
independent_functionElimination,
cut,
applyLambdaEquality,
setElimination,
rename,
hypothesis,
imageMemberEquality,
hypothesisEquality,
baseClosed,
imageElimination,
extract_by_obid,
isectElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
dependent_set_memberEquality,
equalitySymmetry,
computeAll,
instantiate,
cumulativity,
applyEquality,
equalityTransitivity,
because_Cache,
universeEquality
Latex:
\mforall{}[X:CubicalSet]. \mforall{}[I:Cname List]. \mforall{}[f1,f2:I-face(X;I)].
(face-compatible(X;I;f1;f2) {}\mRightarrow{} face-compatible(X;I;f2;f1))
Date html generated:
2017_10_05-AM-10_17_42
Last ObjectModification:
2017_07_28-AM-11_20_26
Theory : cubical!sets
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