Nuprl Lemma : sq_stable__coW-pos-agree
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w':coW(A;a.B[a])].
  ∀p,q:Pos(coW-game(a.B[a];w;w')).  SqStable(coW-pos-agree(a.B[a];w;w';p;q))
Proof
Definitions occuring in Statement : 
coW-pos-agree: coW-pos-agree(a.B[a];w;w';p;q)
, 
coW-game: coW-game(a.B[a];w;w')
, 
coW: coW(A;a.B[a])
, 
sg-pos: Pos(g)
, 
sq_stable: SqStable(P)
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
implies: P 
⇒ Q
, 
nat: ℕ
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
so_lambda: λ2x.t[x]
, 
and: P ∧ Q
, 
prop: ℙ
, 
member: t ∈ T
, 
coW-pos-agree: coW-pos-agree(a.B[a];w;w';p;q)
, 
pi1: fst(t)
, 
sg-pos: Pos(g)
, 
coW-game: coW-game(a.B[a];w;w')
, 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
coW_wf, 
coW-game_wf, 
sg-pos_wf, 
sq_stable__copathAgree, 
sq_stable__le, 
copathAgree_wf, 
nat_wf, 
copath-length_wf, 
le_wf, 
sq_stable__and
Rules used in proof : 
universeEquality, 
functionEquality, 
cumulativity, 
instantiate, 
dependent_functionElimination, 
independent_functionElimination, 
isect_memberEquality, 
because_Cache, 
rename, 
setElimination, 
hypothesis, 
applyEquality, 
lambdaEquality, 
hypothesisEquality, 
productEquality, 
isectElimination, 
extract_by_obid, 
introduction, 
cut, 
thin, 
productElimination, 
sqequalRule, 
sqequalHypSubstitution, 
lambdaFormation, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}'].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[w,w':coW(A;a.B[a])].
    \mforall{}p,q:Pos(coW-game(a.B[a];w;w')).    SqStable(coW-pos-agree(a.B[a];w;w';p;q))
Date html generated:
2018_07_25-PM-01_43_07
Last ObjectModification:
2018_06_20-PM-02_58_40
Theory : co-recursion
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