Nuprl Lemma : coW-pos-agree_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w':coW(A;a.B[a])]. ∀[p,q:Pos(coW-game(a.B[a];w;w'))]. (coW-pos-agree(a.B[a];w;w';p;q) ∈ ℙ)
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),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x.t[x],
and: P ∧ Q,
prop: ℙ,
coW-game: coW-game(a.B[a];w;w'),
pi1: fst(t),
sg-pos: Pos(g),
coW-pos-agree: coW-pos-agree(a.B[a];w;w';p;q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
coW-game_wf,
sg-pos_wf,
copathAgree_wf,
nat_wf,
copath-length_wf,
le_wf
Rules used in proof :
universeEquality,
functionEquality,
cumulativity,
instantiate,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
because_Cache,
rename,
setElimination,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
isectElimination,
extract_by_obid,
productEquality,
thin,
productElimination,
sqequalHypSubstitution,
sqequalRule,
cut,
introduction,
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'))].
(coW-pos-agree(a.B[a];w;w';p;q) \mmember{} \mBbbP{})
Date html generated:
2018_07_25-PM-01_43_02
Last ObjectModification:
2018_06_20-PM-02_47_02
Theory : co-recursion
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