Nuprl Lemma : uanti_sym_wf

`∀[T:Type]. ∀[R:T ⟶ T ⟶ ℙ].  (UniformlyAntiSym(T;x,y.R[x;y]) ∈ ℙ)`

Proof

Definitions occuring in Statement :  uanti_sym: `UniformlyAntiSym(T;x,y.R[x; y])` uall: `∀[x:A]. B[x]` prop: `ℙ` so_apply: `x[s1;s2]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uanti_sym: `UniformlyAntiSym(T;x,y.R[x; y])` so_lambda: `λ2x.t[x]` uimplies: `b supposing a` so_apply: `x[s1;s2]` subtype_rel: `A ⊆r B` so_apply: `x[s]` prop: `ℙ`
Lemmas referenced :  uall_wf isect_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule extract_by_obid sqequalHypSubstitution isectElimination thin cumulativity hypothesisEquality lambdaEquality because_Cache applyEquality functionExtensionality hypothesis axiomEquality equalityTransitivity equalitySymmetry functionEquality universeEquality isect_memberEquality

Latex:
\mforall{}[T:Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].    (UniformlyAntiSym(T;x,y.R[x;y])  \mmember{}  \mBbbP{})

Date html generated: 2016_10_21-AM-09_42_07
Last ObjectModification: 2016_08_01-PM-09_49_15

Theory : rel_1

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