Nuprl Lemma : rels_iso_wf
∀[T,T':Type]. ∀[R:T ⟶ T ⟶ ℙ]. ∀[R':T' ⟶ T' ⟶ ℙ]. ∀[f:T ⟶ T'].  (RelsIso(T;T';x,y.R[x;y];x,y.R'[x;y];f) ∈ ℙ)
Proof
Definitions occuring in Statement : 
rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f)
, 
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 : 
rels_iso: RelsIso(T;T';x,y.R[x; y];x,y.R'[x; y];f)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s1;s2]
, 
so_apply: x[s]
, 
prop: ℙ
Lemmas referenced : 
all_wf, 
iff_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
hypothesis, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
functionEquality, 
isect_memberEquality, 
because_Cache, 
cumulativity, 
universeEquality
Latex:
\mforall{}[T,T':Type].  \mforall{}[R:T  {}\mrightarrow{}  T  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[R':T'  {}\mrightarrow{}  T'  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[f:T  {}\mrightarrow{}  T'].
    (RelsIso(T;T';x,y.R[x;y];x,y.R'[x;y];f)  \mmember{}  \mBbbP{})
Date html generated:
2016_05_15-PM-00_03_09
Last ObjectModification:
2015_12_26-PM-11_25_07
Theory : gen_algebra_1
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