Nuprl Lemma : p-id-compose
∀[A,B:Type]. ∀[f:A ⟶ (B + Top)]. (p-id() o f = f ∈ (A ⟶ (B + Top)))
Proof
Definitions occuring in Statement :
p-id: p-id(),
p-compose: f o g,
uall: ∀[x:A]. B[x],
top: Top,
function: x:A ⟶ B[x],
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
p-compose: f o g,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
bfalse: ff,
prop: ℙ,
do-apply: do-apply(f;x),
p-id: p-id(),
can-apply: can-apply(f;x),
isl: isl(x),
outl: outl(x),
assert: ↑b,
false: False
Lemmas referenced :
top_wf,
can-apply_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
equal_wf,
true_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
because_Cache,
hypothesis,
functionEquality,
cumulativity,
hypothesisEquality,
unionEquality,
extract_by_obid,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
axiomEquality,
universeEquality,
applyEquality,
baseClosed,
lambdaFormation,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
voidElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[f:A {}\mrightarrow{} (B + Top)]. (p-id() o f = f)
Date html generated:
2017_10_01-AM-09_13_56
Last ObjectModification:
2017_07_26-PM-04_49_11
Theory : general
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