Nuprl Lemma : coW-game2_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w,w',w'':coW(A;a.B[a])]. (coW-game2(a.B[a];w;w'';w') ∈ SimpleGame)
Proof
Definitions occuring in Statement :
coW-game2: coW-game2(a.B[a];w;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 :
or: P ∨ Q,
nat: ℕ,
subtype_rel: A ⊆r B,
and: P ∧ Q,
prop: ℙ,
spreadn: spread3,
so_apply: x[s],
so_lambda: λ2x.t[x],
simple-game: SimpleGame,
coW-game2: coW-game2(a.B[a];w;w'';w'),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coW_wf,
copathAgree_wf,
nat_wf,
copath-length_wf,
equal_wf,
or_wf,
copath-nil_wf,
copath_wf
Rules used in proof :
isect_memberEquality,
instantiate,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
universeEquality,
functionEquality,
natural_numberEquality,
addEquality,
rename,
setElimination,
intEquality,
productElimination,
because_Cache,
functionExtensionality,
cumulativity,
independent_pairEquality,
hypothesis,
applyEquality,
lambdaEquality,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
productEquality,
dependent_pairEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w,w',w'':coW(A;a.B[a])]. (coW-game2(a.B[a];w;w'';w') \mmember{} SimpleGame)
Date html generated:
2018_07_25-PM-01_43_21
Last ObjectModification:
2018_06_22-PM-05_14_48
Theory : co-recursion
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