Nuprl Lemma : inject-compose
∀[T:Type]. ∀[f,g:T ⟶ T]. (Inj(T;T;f o g)) supposing (Inj(T;T;g) and Inj(T;T;f))
Proof
Definitions occuring in Statement :
inject: Inj(A;B;f),
compose: f o g,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
inject: Inj(A;B;f),
all: ∀x:A. B[x],
implies: P ⇒ Q,
squash: ↓T,
sq_stable: SqStable(P)
Lemmas referenced :
compose-injections,
inject_wf,
equal_wf,
compose_wf,
sq_stable__inject
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
hypothesis,
cumulativity,
functionExtensionality,
applyEquality,
because_Cache,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
universeEquality,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
imageElimination,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[f,g:T {}\mrightarrow{} T]. (Inj(T;T;f o g)) supposing (Inj(T;T;g) and Inj(T;T;f))
Date html generated:
2017_04_14-AM-07_34_17
Last ObjectModification:
2017_02_27-PM-03_07_28
Theory : fun_1
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