Nuprl Lemma : coW-game_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w':coW(A;a.B[a])]. (coW-game(a.B[a];w;w') ∈ SimpleGame)
Proof
Definitions occuring in Statement :
coW-game: coW-game(a.B[a];w;w'),
coW: coW(A;a.B[a]),
simple-game: SimpleGame,
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
coW-game: coW-game(a.B[a];w;w'),
simple-game: SimpleGame,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
and: P ∧ Q,
or: P ∨ Q,
subtype_rel: A ⊆r B,
nat: ℕ
Lemmas referenced :
copath_wf,
copath-nil_wf,
or_wf,
copathAgree_wf,
equal_wf,
copath-length_wf,
nat_wf,
coW_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
dependent_pairEquality,
productEquality,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
independent_pairEquality,
spreadEquality,
intEquality,
setElimination,
rename,
because_Cache,
cumulativity,
functionEquality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
isect_memberEquality
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w,w':coW(A;a.B[a])]. (coW-game(a.B[a];w;w') \mmember{} SimpleGame)
Date html generated:
2018_07_25-PM-01_42_27
Last ObjectModification:
2018_06_05-AM-11_46_52
Theory : co-recursion
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