Nuprl Lemma : function_functionality_wrt_equipollent_right
∀[A,B,C:Type]. (A ~ B ⇒ C ⟶ A ~ C ⟶ B)
Proof
Definitions occuring in Statement :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
uimplies: b supposing a,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
equipollent_wf,
equipollent_functionality_wrt_equipollent,
function_functionality_wrt_equipollent,
equipollent_weakening_ext-eq,
ext-eq_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
functionEquality,
lambdaEquality,
because_Cache,
independent_functionElimination,
sqequalRule,
independent_isectElimination,
productElimination
Latex:
\mforall{}[A,B,C:Type]. (A \msim{} B {}\mRightarrow{} C {}\mrightarrow{} A \msim{} C {}\mrightarrow{} B)
Date html generated:
2016_10_21-AM-10_57_49
Last ObjectModification:
2016_08_06-PM-03_12_56
Theory : equipollence!!cardinality!
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