Nuprl Lemma : anti_sym_shift

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


Definitions occuring in Statement :  rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f) anti_sym: AntiSym(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 anti_sym: AntiSym(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) all: x:A. B[x] implies:  Q prop: so_apply: x[s1;s2] subtype_rel: A ⊆B so_lambda: λ2y.t[x; y] iff: ⇐⇒ Q and: P ∧ Q
Lemmas referenced :  anti_sym_wf rels_iso_wf inject_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution lambdaFormation hypothesis applyEquality hypothesisEquality sqequalRule lambdaEquality dependent_functionElimination thin axiomEquality universeEquality because_Cache lemma_by_obid isectElimination isect_memberEquality equalityTransitivity equalitySymmetry functionEquality cumulativity independent_functionElimination productElimination

\mforall{}[A,B:Type].  \mforall{}[R:A  {}\mrightarrow{}  A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[S:B  {}\mrightarrow{}  B  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[f:A  {}\mrightarrow{}  B].
    (AntiSym(A;x,y.R[x;y]))  supposing 
          (AntiSym(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_36
Last ObjectModification: 2015_12_26-PM-11_25_04

Theory : gen_algebra_1

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