Nuprl Lemma : proddeq_wf
∀[A,B:Type]. ∀[a:EqDecider(A)]. ∀[b:EqDecider(B)]. (proddeq(a;b) ∈ (A × B) ⟶ (A × B) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
proddeq: proddeq(a;b),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
proddeq: proddeq(a;b),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
prop: ℙ,
iff: P ⇐⇒ Q,
all: ∀x:A. B[x],
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q
Lemmas referenced :
band_wf,
pi1_wf,
pi2_wf,
set_wf,
bool_wf,
all_wf,
iff_wf,
equal_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
setElimination,
rename,
hypothesisEquality,
hypothesis,
productEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[a:EqDecider(A)]. \mforall{}[b:EqDecider(B)]. (proddeq(a;b) \mmember{} (A \mtimes{} B) {}\mrightarrow{} (A \mtimes{} B) {}\mrightarrow{} \mBbbB{})
Date html generated:
2016_05_14-AM-06_07_17
Last ObjectModification:
2015_12_26-AM-11_46_22
Theory : equality!deciders
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