Nuprl Lemma : fun-connected-fixedpoint
∀[T:Type]. ∀[f:T ⟶ T]. ∀[x,y:T]. (x = y ∈ T) supposing (((f y) = y ∈ T) and x is f*(y))
Proof
Definitions occuring in Statement :
fun-connected: y is f*(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
so_lambda: λ2x y.t[x; y],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
and: P ∧ Q,
guard: {T}
Lemmas referenced :
fun-connected-induction,
equal_wf,
and_wf,
fun-connected_wf,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
functionEquality,
cumulativity,
applyEquality,
functionExtensionality,
hypothesis,
independent_functionElimination,
lambdaFormation,
dependent_set_memberEquality,
independent_pairFormation,
applyLambdaEquality,
setElimination,
rename,
productElimination,
equalityTransitivity,
equalitySymmetry,
axiomEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[f:T {}\mrightarrow{} T]. \mforall{}[x,y:T]. (x = y) supposing (((f y) = y) and x is f*(y))
Date html generated:
2018_05_21-PM-07_46_00
Last ObjectModification:
2017_07_26-PM-05_23_32
Theory : general
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