Nuprl Lemma : sq-stable-coW-game-legal1
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w':coW(A;a.B[a])].  ∀p,q:Pos(coW-game(a.B[a];w;w')).  SqStable(Legal1(p;q))
Proof
Definitions occuring in Statement : 
coW-game: coW-game(a.B[a];w;w')
, 
coW: coW(A;a.B[a])
, 
sg-legal1: Legal1(x;y)
, 
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 : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
sq_stable: SqStable(P)
, 
implies: P 
⇒ Q
, 
coW-game: coW-game(a.B[a];w;w')
, 
sg-legal1: Legal1(x;y)
, 
pi2: snd(t)
, 
pi1: fst(t)
, 
sg-pos: Pos(g)
, 
member: t ∈ T
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
squash: ↓T
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
guard: {T}
, 
subtract: n - m
, 
top: Top
, 
le: A ≤ B
, 
not: ¬A
, 
less_than': less_than'(a;b)
, 
true: True
, 
false: False
Lemmas referenced : 
squash_wf, 
sg-legal1_wf, 
coW-game_wf, 
sg-pos_wf, 
coW_wf, 
decidable__int_equal, 
copath-length_wf, 
nat_wf, 
sq_stable__copathAgree, 
equal_wf, 
le_antisymmetry_iff, 
condition-implies-le, 
minus-add, 
minus-one-mul, 
add-swap, 
minus-one-mul-top, 
add-mul-special, 
zero-mul, 
add-zero, 
add-associates, 
add-commutes, 
le-add-cancel, 
copathAgree_wf, 
copath_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
sqequalHypSubstitution, 
sqequalRule, 
productElimination, 
thin, 
cut, 
introduction, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
lambdaEquality, 
applyEquality, 
hypothesis, 
instantiate, 
cumulativity, 
functionEquality, 
universeEquality, 
dependent_functionElimination, 
setElimination, 
rename, 
addEquality, 
because_Cache, 
natural_numberEquality, 
unionElimination, 
imageElimination, 
inlFormation, 
independent_pairFormation, 
independent_functionElimination, 
promote_hyp, 
equalitySymmetry, 
hyp_replacement, 
applyLambdaEquality, 
intEquality, 
independent_isectElimination, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
minusEquality, 
multiplyEquality, 
imageMemberEquality, 
baseClosed, 
productEquality, 
inrFormation
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(Legal1(p;q))
Date html generated:
2019_06_20-PM-00_57_46
Last ObjectModification:
2019_01_02-PM-01_34_27
Theory : co-recursion-2
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