Nuprl Lemma : sq_stable__assoc
∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. SqStable(Assoc(T;op))
Proof
Definitions occuring in Statement :
assoc: Assoc(T;op),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
assoc: Assoc(T;op),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
implies: P ⇒ Q,
sq_stable: SqStable(P),
prop: ℙ
Lemmas referenced :
sq_stable__uall,
uall_wf,
equal_wf,
sq_stable__equal,
squash_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[op:T {}\mrightarrow{} T {}\mrightarrow{} T]. SqStable(Assoc(T;op))
Date html generated:
2019_06_20-PM-00_27_08
Last ObjectModification:
2018_08_07-PM-01_33_41
Theory : fun_1
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