Nuprl Lemma : sq_stable__fun_thru_2op
∀[A,B:Type]. ∀[opa:A ⟶ A ⟶ A]. ∀[opb:B ⟶ B ⟶ B]. ∀[f:A ⟶ B]. SqStable(FunThru2op(A;B;opa;opb;f))
Proof
Definitions occuring in Statement :
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
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,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[opa:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[opb:B {}\mrightarrow{} B {}\mrightarrow{} B]. \mforall{}[f:A {}\mrightarrow{} B].
SqStable(FunThru2op(A;B;opa;opb;f))
Date html generated:
2016_05_15-PM-00_02_50
Last ObjectModification:
2015_12_26-PM-11_25_19
Theory : gen_algebra_1
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