Nuprl Lemma : p-compose-associative
∀[A,B,C,D:Type]. ∀[h:A ⟶ (B + Top)]. ∀[g:B ⟶ (C + Top)]. ∀[f:C ⟶ (D + Top)].
(f o g o h = f o g o h ∈ (A ⟶ (D + Top)))
Proof
Definitions occuring in Statement :
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,
do-apply: do-apply(f;x),
can-apply: can-apply(f;x),
all: ∀x:A. B[x],
implies: P ⇒ Q,
isl: isl(x),
outl: outl(x),
ifthenelse: if b then t else f fi ,
btrue: tt,
bfalse: ff,
prop: ℙ
Lemmas referenced :
top_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
sqequalRule,
applyEquality,
hypothesisEquality,
cumulativity,
thin,
unionEquality,
extract_by_obid,
hypothesis,
lambdaFormation,
unionElimination,
because_Cache,
inrEquality,
sqequalHypSubstitution,
isectElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
functionEquality,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[A,B,C,D:Type]. \mforall{}[h:A {}\mrightarrow{} (B + Top)]. \mforall{}[g:B {}\mrightarrow{} (C + Top)]. \mforall{}[f:C {}\mrightarrow{} (D + Top)].
(f o g o h = f o g o h)
Date html generated:
2017_10_01-AM-09_14_00
Last ObjectModification:
2017_07_26-PM-04_49_15
Theory : general
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