Nuprl Lemma : one_or_both_ind_wf
∀[X:𝕌{j}]. ∀[A,B:Type]. ∀[x:one_or_both(A;B)]. ∀[both:bval:(A × B) ⟶ X]. ∀[left:lval:A ⟶ X]. ∀[right:rval:B ⟶ X].
(one_or_both_ind(x;bval.both[bval];lval.left[lval];rval.right[rval]) ∈ X)
Proof
Definitions occuring in Statement :
one_or_both_ind: one_or_both_ind(x;bval.both[bval];lval.left[lval];rval.right[rval]),
one_or_both: one_or_both(A;B),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
one_or_both: one_or_both(A;B),
one_or_both_ind: one_or_both_ind(x;bval.both[bval];lval.left[lval];rval.right[rval]),
so_apply: x[s]
Lemmas referenced :
one_or_both_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
sqequalRule,
unionElimination,
thin,
productElimination,
applyEquality,
hypothesisEquality,
independent_pairEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
isect_memberEquality,
isectElimination,
because_Cache,
productEquality,
lemma_by_obid,
universeEquality
Latex:
\mforall{}[X:\mBbbU{}\{j\}]. \mforall{}[A,B:Type]. \mforall{}[x:one\_or\_both(A;B)]. \mforall{}[both:bval:(A \mtimes{} B) {}\mrightarrow{} X]. \mforall{}[left:lval:A {}\mrightarrow{} X].
\mforall{}[right:rval:B {}\mrightarrow{} X].
(one\_or\_both\_ind(x;bval.both[bval];lval.left[lval];rval.right[rval]) \mmember{} X)
Date html generated:
2016_05_15-PM-05_32_32
Last ObjectModification:
2015_12_27-PM-02_10_09
Theory : general
Home
Index