Nuprl Lemma : xxanti_sym_functionality_wrt_breqv
∀[T:Type]. ∀[R,R':T ⟶ T ⟶ ℙ]. uiff(anti_sym(T;R);anti_sym(T;R')) supposing R <≡>{T} R'
Proof
Definitions occuring in Statement :
xxanti_sym: anti_sym(T;R),
binrel_eqv: E <≡>{T} E',
uiff: uiff(P;Q),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
xxanti_sym: anti_sym(T;R),
binrel_eqv: E <≡>{T} E',
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
anti_sym: AntiSym(T;x,y.R[x; y]),
all: ∀x:A. B[x],
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
anti_sym_wf,
iff_weakening_uiff,
anti_sym_functionality_wrt_iff,
uiff_wf,
all_wf,
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
axiomEquality,
applyEquality,
universeEquality,
because_Cache,
lemma_by_obid,
isectElimination,
addLevel,
productElimination,
independent_isectElimination,
independent_functionElimination,
lambdaFormation,
cumulativity,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality
Latex:
\mforall{}[T:Type]. \mforall{}[R,R':T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. uiff(anti\_sym(T;R);anti\_sym(T;R')) supposing R <\mequiv{}>\{T\} R'
Date html generated:
2016_05_15-PM-00_01_06
Last ObjectModification:
2015_12_26-PM-11_26_55
Theory : gen_algebra_1
Home
Index