Nuprl Lemma : p-fun-exp-one
∀[A:Type]. ∀[f:A ⟶ (A + Top)]. (f^1 = f ∈ (A ⟶ (A + Top)))
Proof
Definitions occuring in Statement :
p-fun-exp: f^n,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
union: left + right,
natural_number: $n,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
p-fun-exp: f^n,
all: ∀x:A. B[x],
member: t ∈ T,
top: Top,
uall: ∀[x:A]. B[x],
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q
Lemmas referenced :
primrec1_lemma,
equal_wf,
squash_wf,
true_wf,
top_wf,
p-compose-id,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
isect_memberFormation,
applyEquality,
lambdaEquality,
imageElimination,
isectElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
functionEquality,
cumulativity,
unionEquality,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
independent_isectElimination,
productElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[A:Type]. \mforall{}[f:A {}\mrightarrow{} (A + Top)]. (f\^{}1 = f)
Date html generated:
2017_10_01-AM-09_14_25
Last ObjectModification:
2017_07_26-PM-04_49_32
Theory : general
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