Nuprl Lemma : product_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,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
equipollent: A ~ B,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
biject: Bij(A;B;f),
and: P ∧ Q,
inject: Inj(A;B;f),
surject: Surj(A;B;f),
all: ∀x:A. B[x],
pi2: snd(t),
pi1: fst(t),
guard: {T}
Lemmas referenced :
exists_wf,
biject_wf,
pi2_wf,
pi1_wf,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
lemma_by_obid,
isectElimination,
functionEquality,
hypothesisEquality,
lambdaEquality,
hypothesis,
universeEquality,
dependent_pairFormation,
spreadEquality,
independent_pairEquality,
applyEquality,
productEquality,
independent_pairFormation,
promote_hyp,
because_Cache,
equalityUniverse,
levelHypothesis,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}[A,B,C:Type]. (A \msim{} B {}\mRightarrow{} C \mtimes{} A \msim{} C \mtimes{} B)
Date html generated:
2016_05_14-PM-03_59_59
Last ObjectModification:
2015_12_26-PM-07_44_37
Theory : equipollence!!cardinality!
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