Nuprl Lemma : uanti_sym_shift

[A,B:Type]. ∀[R:A ⟶ A ⟶ ℙ]. ∀[S:B ⟶ B ⟶ ℙ]. ∀[f:A ⟶ B].
  (UniformlyAntiSym(A;x,y.R[x;y])) supposing 
     (UniformlyAntiSym(B;x,y.S[x;y]) and 
     RelsIso(A;B;x,y.R[x;y];x,y.S[x;y];f) and 


Definitions occuring in Statement :  rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f) uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]) inject: Inj(A;B;f) uimplies: supposing a uall: [x:A]. B[x] prop: so_apply: x[s1;s2] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a uanti_sym: UniformlyAntiSym(T;x,y.R[x; y]) rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f) inject: Inj(A;B;f) prop: so_apply: x[s1;s2] so_lambda: λ2y.t[x; y] all: x:A. B[x] implies:  Q iff: ⇐⇒ Q and: P ∧ Q
Lemmas referenced :  uanti_sym_wf rels_iso_wf inject_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution hypothesis applyEquality hypothesisEquality sqequalRule isect_memberEquality isectElimination thin axiomEquality because_Cache equalityTransitivity equalitySymmetry lemma_by_obid lambdaEquality functionEquality cumulativity universeEquality dependent_functionElimination independent_functionElimination independent_isectElimination productElimination

\mforall{}[A,B:Type].  \mforall{}[R:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[S:B  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[f:A  {}\mrightarrow{}  B].
    (UniformlyAntiSym(A;x,y.R[x;y]))  supposing 
          (UniformlyAntiSym(B;x,y.S[x;y])  and 
          RelsIso(A;B;x,y.R[x;y];x,y.S[x;y];f)  and 

Date html generated: 2016_05_15-PM-00_03_39
Last ObjectModification: 2015_12_26-PM-11_25_03

Theory : gen_algebra_1

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