Nuprl Lemma : sq_stable__action_p
∀[A:Type]. ∀[x:A ⟶ A ⟶ A]. ∀[e:A]. ∀[S:Type]. ∀[f:A ⟶ S ⟶ S]. SqStable(IsAction(A;x;e;S;f))
Proof
Definitions occuring in Statement :
action_p: IsAction(A;x;e;S;f),
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
action_p: IsAction(A;x;e;S;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
sq_stable: SqStable(P),
and: P ∧ Q
Lemmas referenced :
sq_stable__and,
uall_wf,
all_wf,
equal_wf,
sq_stable__uall,
sq_stable__all,
sq_stable__equal,
squash_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
isect_memberEquality,
independent_functionElimination,
because_Cache,
lambdaFormation,
dependent_functionElimination,
axiomEquality,
productElimination,
independent_pairEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}[x:A {}\mrightarrow{} A {}\mrightarrow{} A]. \mforall{}[e:A]. \mforall{}[S:Type]. \mforall{}[f:A {}\mrightarrow{} S {}\mrightarrow{} S]. SqStable(IsAction(A;x;e;S;f))
Date html generated:
2016_05_15-PM-00_02_35
Last ObjectModification:
2015_12_26-PM-11_25_42
Theory : gen_algebra_1
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