Nuprl Lemma : sumdeq_wf
∀[A,B:Type]. ∀[a:EqDecider(A)]. ∀[b:EqDecider(B)]. (sumdeq(a;b) ∈ (A + B) ⟶ (A + B) ⟶ 𝔹)
Proof
Definitions occuring in Statement :
sumdeq: sumdeq(a;b),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
sumdeq: sumdeq(a;b),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q
Lemmas referenced :
bfalse_wf,
equal_wf,
set_wf,
bool_wf,
all_wf,
iff_wf,
assert_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lambdaEquality,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
thin,
unionEquality,
lambdaFormation,
unionElimination,
applyEquality,
setElimination,
rename,
sqequalHypSubstitution,
extract_by_obid,
isectElimination,
dependent_functionElimination,
independent_functionElimination,
axiomEquality,
functionEquality,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[a:EqDecider(A)]. \mforall{}[b:EqDecider(B)]. (sumdeq(a;b) \mmember{} (A + B) {}\mrightarrow{} (A + B) {}\mrightarrow{} \mBbbB{})
Date html generated:
2019_06_20-PM-00_32_02
Last ObjectModification:
2018_08_21-PM-01_53_07
Theory : equality!deciders
Home
Index