Nuprl Lemma : strict-fun-connected-step
∀[T:Type]. ∀f:T ⟶ T. ∀x:T. f x = f+(x) supposing ¬((f x) = x ∈ T)
Proof
Definitions occuring in Statement :
strict-fun-connected: y = f+(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
not: ¬A,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
strict-fun-connected: y = f+(x),
and: P ∧ Q,
cand: A c∧ B,
decidable: Dec(P),
guard: {T},
or: P ∨ Q
Lemmas referenced :
equal_wf,
fun-connected-step,
not_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
voidElimination,
extract_by_obid,
isectElimination,
cumulativity,
applyEquality,
functionExtensionality,
hypothesis,
rename,
independent_functionElimination,
equalitySymmetry,
independent_pairFormation,
because_Cache,
inrFormation,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. \mforall{}x:T. f x = f+(x) supposing \mneg{}((f x) = x)
Date html generated:
2018_05_21-PM-07_45_17
Last ObjectModification:
2017_07_26-PM-05_22_42
Theory : general
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