### 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

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