Nuprl Lemma : sq_stable__ident
∀[T:Type]. ∀[op:T ⟶ T ⟶ T]. ∀[id:T]. SqStable(Ident(T;op;id))
Proof
Definitions occuring in Statement :
ident: Ident(T;op;id),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
ident: Ident(T;op;id),
uall: ∀[x:A]. B[x],
member: t ∈ T,
sq_stable: SqStable(P),
implies: P ⇒ Q,
and: P ∧ Q,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
prop: ℙ
Lemmas referenced :
squash_wf,
uall_wf,
and_wf,
equal_wf,
sq_stable__uall,
sq_stable__and,
sq_stable__equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
isect_memberEquality,
isectElimination,
productElimination,
independent_pairEquality,
axiomEquality,
hypothesis,
lemma_by_obid,
applyEquality,
because_Cache,
functionEquality,
universeEquality,
independent_functionElimination,
lambdaFormation
Latex:
\mforall{}[T:Type]. \mforall{}[op:T {}\mrightarrow{} T {}\mrightarrow{} T]. \mforall{}[id:T]. SqStable(Ident(T;op;id))
Date html generated:
2016_05_15-PM-00_02_16
Last ObjectModification:
2015_12_26-PM-11_25_39
Theory : gen_algebra_1
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