Nuprl Lemma : injection-composition
∀[A,B,C:Type]. ∀[f:A ⟶ B]. ∀[g:B ⟶ C]. (Inj(A;C;g o f)) supposing (Inj(B;C;g) and Inj(A;B;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 :
inject: Inj(A;B;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
guard: {T},
compose: f o g
Lemmas referenced :
equal_wf,
compose_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
applyEquality,
functionExtensionality,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
because_Cache,
functionEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
independent_functionElimination
Latex:
\mforall{}[A,B,C:Type]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[g:B {}\mrightarrow{} C]. (Inj(A;C;g o f)) supposing (Inj(B;C;g) and Inj(A;B;f))
Date html generated:
2017_04_14-AM-07_34_19
Last ObjectModification:
2017_02_27-PM-03_07_30
Theory : fun_1
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